
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
Let \(A_{1}, A_{2}, A_{3}, A_{4}, A_{5}\), and \(A_{6}\) be six points on a circle in this order such that \(\overline{A_{1} A_{2}}=\overline{A_{2} A_{3}}\), \(\widehat{A_{3} A_{4}}=\widehat{A_{4} A_{5}}\), and \(\widehat{A_{5} A_{6}}=\widehat{A_{6} A_{1}}\), where \(\widehat{A_{1} A_{2}}\) denotes the arc length of the arc \(A_{1} A_{2}\) etc. It is also known that \(\angle A_{1} A_{3} A_{5}=72^{\circ}\). Find the size of \(\angle A_{4} A_{6} A_{2}\) in degrees.

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