
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 that $J_k = 10\dots 0128$ where there are $k$ zeros between the $1$ and the $128$, determine the maximum value of the number of factors of $2$ in the prime factorization of $J_k$.

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