
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 functions $f(x)= \frac{x}{e^{x}}$ and $g(x)= e^{x-1} - \frac{1}{x} - \ln x - x + a$.
1. Find the maximum value of $f(x)$.
2. If the curve of $y = g(x)$ is tangent to the x-axis, find the value of $a$.

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