
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 general term formula of the sequence $\{a_n\}$ is given by ${a_n = \frac{8}{3} \cdot \left(\frac{1}{8}\right)^n - 3 \cdot \left(\frac{1}{4}\right)^n + \left(\frac{1}{2}\right)^n}$. If $a_n \leqslant a_m$, then $m=$____.

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