
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 a sequence $\{a_n\}$ satisfying $a_1=1$ and $a_{n+1}= \begin{cases} 2a_{n}, & \text{if } n \text{ is an odd positive integer} \\ a_{n}+1, & \text{if } n \text{ is an even positive integer} \end{cases},$ determine in which term in the sequence the term is 254.

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