
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 numbers $\log(a^2b^4)$, $\log(a^6b^9)$, and $\log(a^{10}b^{14})$ form the first three terms of an arithmetic sequence, and the $10^\text{th}$ term of this sequence is $\log(a^n)$. Determine the value of $n$.

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