
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
Consider an arithmetic sequence $\{a_n\}$ with the sum of the first $n$ terms denoted as $S_n$. Given that $a_3 = 24$ and $a_6 = 18$,

(Ⅰ) Find the general formula for the $n$th term of the sequence $\{a_n\}$,
(Ⅱ) Find the sum of the first $n$ terms $S_n$ for the sequence $\{a_n\}$,
(Ⅲ) Determine the value of $n$ for which $S_n$ is maximized, and calculate the maximum value of $S_n$.

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