
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
If for any real number \( x \), \( f(x)=\log _{a}\left(2+\mathrm{e}^{x-1}\right) \leqslant-1 \), then the range of the real number \( a \) is ___. (Where \( e \) is an irrational number, \( e=2.71828 \cdots \))

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