
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
Given \( a_{1}=3 \) and \( b_{1}=100 \), for \( n \geqslant 1 \):
\[ 
a_{n+1}=3^{a_n} 
\]
\[ 
b_{n+1}=100^{b_n} 
\]

Find the smallest positive integer \( m \) such that \( b_m > a_{100} \).

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