
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 \( f(x) = \frac{4 e^{x-1}}{x+1} + x^2 - 3ax + a^2 - 1 \), if there exists \( x_0 > 0 \) such that \( f(x_0) \leq 0 \), find the minimum possible value of the real number \( a \).

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