
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 the sequence \( a_i \) be defined as \( a_{i+1} = 2^{a_i} \). Find the number of integers \( 1 \leq n \leq 1000 \) such that if \( a_0 = n \), then 100 divides \( a_{1000} - a_1 \).

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