
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 sequence of numbers defined recursively by $s_1=1$ and for $m>1$ by $s_m=1+s_{m/2}$ when $m$ is even and by $s_m=\frac{1}{s_{m-1}}$ when $m$ is odd. Given that $s_m=\frac{17}{99}$, find $m$.

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