
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
The expression  $\sin2^\circ\sin4^\circ\sin6^\circ\cdots\sin90^\circ$  is equal to  $p\sqrt{5}/2^{50}$ , where  $p$  is an integer. Find  $p$ .

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