
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
Consider the following algorithm.

Step 0. Set \( n = m \).

Step 1. If \( n \) is even, divide \( n \) by two. If \( n \) is odd, increase \( n \) by one.

Step 2. If \( n > 1 \), go to Step 1. If \( n = 1 \), end the algorithm. How many natural numbers \( m \) exist such that Step 1 will be performed exactly 15 times when this algorithm is executed?

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