
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 $f(x) = \ln x - x + 1$, $x \in (0, +\infty)$, and $g(x) = e^{x} - ax$. Find:

1. The maximum value of $f(x)$.
2. The range of values for $a$ such that for all $x_{1} \in (0, +\infty)$, there exists $x_{2} \in [1,2]$ satisfying $f(x_{1}) \leq g(x_{2})$.

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