
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 $\{a_n\}$ is an increasing arithmetic sequence with $a_3 = \frac{5}{2}$, and $a_2a_4=6$.
1. Find the first term $a_1$ and the common difference $d$.
2. Find the general term $a_n$ and the sum of the first $n$ terms $S_n$.

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