
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 $u_1 = 2$ and for $m > 1$ by $u_m = 2 + u_{m/3}$ when $m$ is divisible by 3 and by $u_m = \frac{1}{u_{m-1}}$ when $m$ is not divisible by 3. Given that $u_m = \frac{7}{24}$, find $m$.

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