
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
For which positive integer values of \( k \) does the number 1 appear among the elements of the sequence \(\left(a_{n}\right)\), where \( a_{1}=k \) and \( a_{n+1}=\frac{a_{n}}{2} \) if \( a_{n} \) is even, and \( a_{n+1}=a_{n}+5 \) if \( a_{n} \) is odd?

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