
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
It is known that a regular \( n \)-gon can be constructed with straightedge and compass if \( n \) is a prime that is 1 plus a power of 2. It is also possible to construct a \( 2n \)-gon whenever an \( n \)-gon is constructible, or a \( p_{1}p_{2} \cdots p_{m} \)-gon where the \( p_{i} \)'s are distinct primes of the above form. What is the largest \( n \) less than 4,300,000,000 such that a regular \( n \)-gon is constructible?

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