
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
Given that the common difference $d$ of the arithmetic sequence $\{a\_n\}$ is less than 0, and $a\_2 \cdot a\_4 = 12$, $a\_1 + a\_5 = 8$. Find:
1. The first term $a\_1$ and the common difference $d$;
2. The sum $S_{10}$ of the first 10 terms of the sequence.

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