
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
Consider the function $f(x)=e^{x+1}-mx$, and $g(x)=ae^x-x$ (where $m$ and $a$ are real numbers). If there exists a real number $a$ such that $f(x) \leq g(x)$ for all $x \in \mathbb{R}$, determine the range of values for the real number $m$.

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