
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 the function $f(x) = ae^{x} - 2x + 1$.
1. Discuss the monotonicity of $f(x)$.
2. For the function $g(x) = f(x) + x\ln{x}$, when $a > 0$, discuss the number of zeros of $g(x)$.

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