
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
If  $\displaystyle\prod_{i=6}^{2021} (1-\tan^2((2^i)^\circ))$  can be written in the form  $a^b$  for positive integers  $a,b$  with  $a$  squarefree, find  $a+b$ .

*Proposed by Deyuan Li and Andrew Milas*

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