
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
The sequence $\{a_n\}$ is an arithmetic sequence where $a_1 = -3$, and $11a_5 = 5a_8 - 13$.
(1) Find the common difference $d$;
(2) Find the minimum value of the sum of the first $n$ terms $S_n$.

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