
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 \( f(x)=x \ln x - \frac{1}{3} a x^{3} + 2x \) where \( a > 0 \):
1. If \( f(x) \leq 1 \) always holds, find the minimum value of \( a \).
2. If \( f(x) \) has a maximum value, find the range of \( a \).

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