
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 $\{a_n\}$ that satisfies ${5}^{a_{n+1}}=25\cdot{5}^{a_{n}}$, and ${a}_{2}+{a}_{4}+{a}_{6}=9$, find the value of ${\log }_{\frac{1}{3}}({a}_{5}+{a}_{7}+{a}_{9})$.

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