
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
The sequence \(\left(a_{n}\right)\) is defined as follows:

\[ a_{1}=k \text{ (positive integer)}, \]

\[ a_{n+1}= \begin{cases}a_{n} / 2, & \text{if } a_{n} \text{ is even} \\ a_{n}+5, & \text{if } a_{n} \text{ is odd. }\end{cases} \]

For which positive integers \(k\) does the number 1 appear among the terms of the sequence \(\left(a_{n}\right)\)?

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