
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
Consider the function $f(x) = 2a\ln x - x^2 + a$.
(I) Discuss the monotonicity of the function $f(x)$.
(II) If the function $f(x)$ satisfies $f(x) \leq 0$ within its domain, find the range of the real number $a$.

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