
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
Construct the pentagon \( A_{1} A_{2} A_{3} A_{4} A_{5} \) if the reflection of point \( A_{i} \) on point \( A_{i+1} \) is given for \( i = 1, \ldots, 5 \), with \( A_{6} := A_{1} \).

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