
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 \( f(x) = \mathrm{e}^x \left( x^3 - 3x + 3 \right) - a \mathrm{e}^x - x \) where \( x \geq -2 \), if the inequality \( f(x) \leq 0 \) has a solution, determine the minimum value of the real number \( a \).

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