
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 $\{a_n\}$, $a_{10}=18$, and the sum of the first 5 terms $S_5=-15$.
(1) Find the general term formula for sequence $\{a_n\}$;
(2) Find the minimum value of the sum of the first $n$ terms for the sequence $\{a_n\}$, and state when the minimum is achieved.

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