
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
In the arithmetic sequence $\{a_n\}$, it is given that $(a_3 + a_4 = 15, a_2 \cdot a_5 = 54)$, and the common difference $d < 0$.

(1) Find the general term formula $a_n$;

(2) Find the maximum value of the sum $S_n$ of the first $n$ terms and the corresponding $n$ value.

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