
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 the sequence $\{a_n\}$ which satisfies $5^{a_{n+1}} = 25 \cdot 5^{a_n}$, and $a_2 + a_4 + a_6 = 9$, calculate $\log_{\frac{1}{3}}(a_5 + a_7 + a_9)$.

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