
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 $f(x) = e^x - ax - 1$.
(1) Find the intervals where $f(x)$ is monotonically increasing.
(2) Determine whether there is a value of $a$ such that $f(x)$ is a decreasing function on the interval $(-2, 3)$. If such value exists, find the range of $a$. If not, explain why.

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