
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 a monotonically increasing arithmetic sequence, where $a_1$ and $a_2$ are the two real roots of the equation $e^{2x} - 6e^{x} + 8 = 0$.
(1) Find the general term formula for the sequence $\{a_n\}$.
(2) Let $b_n = e^{a_n}$, find the sum of the first $n$ terms, $S_n$, of the sequence $\{b_n\}$.

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