### Component 1 (Lines 1-20)
- **Description:** Simplifying the innermost radical √(1/4096).
- **Plan:** Lines 1-8
- **Prompt:** Compute the square root of 1/4096 as per the above plan.
- **Execution:** Lines 9-18
- **Comment:** Lines 19-20

### Component 2 (Lines 21-28)
- **Description:** Simplifying the next radical √(³√(1/64)).
- **Plan:** Lines 21-23
- **Prompt:** Compute the cube root of 1/64 as per the above plan.
- **Execution:** Lines 24-27
- **Comment:** Lines 28

### Component 3 (Lines 30-33)
- **Description:** Simplifying the final radical √(1/4).
- **Plan:** Lines 30
- **Prompt:** Compute the square root of 1/4 as per the above plan.
- **Execution:** Lines 31-32
- **Comment:** Lines 33

### Component 4 (Lines 35-41)
- **Description:** Verifying the steps of the simplification process.
- **Plan:** Lines 35
- **Prompt:** Verify each step of the simplification process as per the above plan.
- **Execution:** Lines 36-40
- **Comment:** Lines 41

### Component 5 (Lines 43-54)
- **Description:** Proposing and executing an alternative method using exponents.
- **Plan:** Lines 43-48
- **Prompt:** Express the original expression using exponents and simplify as per the above plan.
- **Execution:** Lines 49-54
- **Comment:** Lines not found

### Component 6 (Lines 56-63)
- **Description:** Computing (1/4096)^(1/12) using the exponent method.
- **Plan:** Lines 56-60
- **Prompt:** Compute (1/4096)^(1/12) using the exponent method as per the above plan.
- **Execution:** Lines 61-63
- **Comment:** Lines not found

### Component 7 (Lines 65-66)
- **Description:** Commenting on the results of both methods.
- **Plan:** Lines not found
- **Prompt:** Comment on the results of both methods.
- **Execution:** Lines not found
- **Comment:** Lines 65-66

### Component 8 (Lines 68-81)
- **Description:** Final verification and conclusion.
- **Plan:** Lines 68
- **Prompt:** Verify the final result using both methods and conclude as per the above plan.
- **Execution:** Lines 69-74
- **Comment:** Lines 75-81