
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
At a recent math contest, Evan was asked to find \( 2^{2016} (\bmod p) \) for a given prime number \( p \) where \( 100 < p < 500 \). Evan first tried taking 2016 modulo \( p-1 \), resulting in a value \( e \) larger than 100. Evan noted that \( e - \frac{1}{2}(p-1) = 21 \) and then realized the answer was \( -2^{21} (\bmod p) \). What was the prime \( p \)?

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