
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 that the sum of the first $n$ terms of the sequence $\{a\_n\}$ is $S\_n$ and $6S\_n = 9a\_n - 1$.
(I) Find the general term formula of the sequence $\{a\_n\}$;
(II) If the function $f(x) = A\sin(ωx + φ) (A > 0, ω > 0, 0 < φ < π)$ has a period of $π$, and it reaches its maximum at $x = \frac{π}{6}$, with the maximum value being $a\_3$, find the analytic expression of the function $f(x)$.

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