
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Point \( A \) is subjected to central symmetry with center at point \( O \), resulting in point \( A' \). Then point \( A' \) is subjected to central symmetry with center at another point \( O' \), resulting in point \( A'' \). Find the distance between \( A \) and \( A'' \) if the distance between \( O \) and \( O' \) is \( a \).

Present the answer in LaTex format: \boxed{Your answer}
user