
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
Let \( f(x) = A\left(x^{2}-2x\right)e^{x} - e^{x} + 1 \). For any \( x \leq 0 \), it holds that \( f(x) \geq 0 \). Determine the range of the real number \( A \).

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