
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
Let $g(n)$ be the base-3 logarithm of the sum of the elements of the $n$th row in Pascal-like triangle, where each row's sum grows as $3^n$. Express $\frac{g(n)}{\log_{10} 3}$ in terms of $n$. Assume the growth pattern follows from a similar combinatory logic of subsets but with tripled recursive relationships instead of doubled.

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