
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
Define \( J(m) = 10^5 + m \), where \( m = 2^a \) for some non-negative integer \( a \). Let \( M(a) \) denote the number of factors of 2 in the prime factorization of \( J(m) \). Determine the maximum value of \( M(a) \) for \( a \geq 0 \).

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