
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 $\left\{a_{n}\right\}$ with the sum of the first $n$ terms denoted as $S_{n}$. It is given that $a_{3} = 12$, $S_{12} > 0$, and $S_{13} < 0$.
(1) Determine the range of values for the common difference $d$.
(2) Identify which of $S_{1}, S_{2}, \cdots, S_{12}$ is the largest value and provide a justification.

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