
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
(2014·Zhengzhou Simulation) Given the functions $f(x)=e^x+ax, g(x)=ax-\ln x$, where $a\leq 0$.

(1) Find the extremum of $f(x)$.

(2) If there exists an interval $M$ such that $f(x)$ and $g(x)$ have the same monotonicity on interval $M$, find the range of values for $a$.

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