
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
If a positive integer \( a \) is input into a machine, where the output is \( a+3 \) if \( a \) is odd and \( a+5 \) if \( a \) is even, and this process is repeated 51 times with the initial input \( a = 15 \), calculate the final output.

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