<Question>
If $a+b=8$, $b+c=-3$, and $a+c= -5$, what is the value of the product $abc$?
</Question>

<think>
<Plan_1>
Okay, let me try to solve this system of equations. So, we have three equations:

1. a + b = 8
2. b + c = -3
3. a + c = -5

And we need to find the product abc. Hmm, since there are three variables and three equations, I think I can solve for each variable step by step.

First, maybe I can express one variable in terms of another from one equation and substitute it into another. Let's see.

Looking at the first equation, a + b = 8. Maybe I can solve for a here.
So, a = 8 - b. That seems straightforward.

Now, let's look at the third equation, a + c = -5. Since I already have a in terms of b, I can substitute that into this equation.

<prompt_1.1> Substitute the expression for a from the first equation into the third equation. </prompt_1.1>
-----

Now, let's check if these values satisfy all three equations.

<prompt_1.2> Verify the solution by checking if the values of a, b, and c satisfy all three equations. </prompt_1.2>
</Plan_1>

<Execution_1>
<execution_1.1>
Substituting a = 8 - b into the third equation gives:

(8 - b) + c = -5

Simplify that: 8 - b + c = -5. Let's rearrange it to group like terms. Maybe move the 8 to the other side:

-b + c = -5 - 8
-b + c = -13

Hmm, so that's equation 4: -b + c = -13.
</execution_1.1>

<execution_1.2>
First equation: a + b = -12 + 4 = -8. Wait, that's supposed to be 8. Oh no, that's not right. Did I make a mistake here?
</execution_1.2>
</Execution_1>

<Plan_2>
Based on execution_1.1:
But we also have the second equation: b + c = -3. Let's write that down as equation 2.

So now, we have two equations with b and c:

<prompt_2.1> Use the second and fourth equations to solve for b and c. </prompt_2.1>
-----

Based on execution_1.2:
Let me check my steps again.

<prompt_2.2> Re-evaluate the solution process to check for mistakes in solving the equations. </prompt_2.2>
</Plan_2>

<Execution_2>
<execution_2.1>
1. b + c = -3
2. -b + c = -13

If I add these two equations together, the b terms will cancel out. Let's try that:

(b + c) + (-b + c) = -3 + (-13)
b - b + c + c = -16
0 + 2c = -16
2c = -16
c = -8

Wait, so c is -8? Let me check that.
</execution_2.1>

<execution_2.2>
Starting with a + b = 8. So a = 8 - b. Then substitute into a + c = -5:

(8 - b) + c = -5. That's 8 - b + c = -5. Subtract 8 from both sides: -b + c = -13. That's correct. Then the second equation is b + c = -3. So we have:

-b + c = -13

b + c = -3

If we add these two equations together, the b terms cancel:

(-b + c) + (b + c) = -13 + (-3)

Which simplifies to:

0b + 2c = -16

So 2c = -16, so c = -8. Then plug back into b + c = -3:

b + (-8) = -3 → b = -3 + 8 = 5. Then a = 8 - b = 8 - 5 = 3. So a=3, b=5, c=-8.
</execution_2.2>
</Execution_2>

<Plan_3>
Based on execution_2.1:
Then plug back into equation 2: b + c = -3. So b + (-8) = -3 → b = -3 + 8 = 5. So b is 5?

Wait, let me confirm. If c is -8, then from equation 2: b + (-8) = -3 → b = -3 + 8 → b = 5.
-----

Based on execution_2.2:
Then a + b = 3 + 5 = 8, which matches the first equation. b + c = 5 + (-8) = -3, which matches the second equation. a + c = 3 + (-8) = -5, which matches the third equation.

Therefore, the values are a=3, b=5, c=-8. So the product abc is 3 * 5 * (-8).
Let's compute that: 3*5=15, 15*(-8)= -120.

Wait, but the question asks for the product abc. So is it -120?

But wait, let me double-check the values again. Maybe I made a mistake in solving.

<prompt_3.1> Perform a final verification of the solution and confirm the product abc. </prompt_3.1>
</Plan_3>

<Execution_3>
<execution_3.1>
Let me write down all the steps again to verify:

1. a + b = 8 → a = 8 - b

3. a + c = -5 → (8 - b) + c = -5 → 8 - b + c = -5 → -b + c = -13

2. b + c = -3

So, we have:

-b + c = -13

b + c = -3

Adding both equations:

(-b + c) + (b + c) = -13 + (-3)

0b + 2c = -16 → 2c = -16 → c = -8

Then from equation 2: b + (-8) = -3 → b = 5

From equation 1: a = 8 - 5 = 3

Thus, a=3, b=5, c=-8. Product abc= 3*5*(-8)= -120.

Yes, that seems correct.
</execution_3.1>
</Execution_3>

<Final_answer>
Therefore, the value of the product $abc$ is $\boxed{-120}$.
</Final_answer>
</think>