
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 $f(x) = a\ln x - x^2$, $g(x) = (\lambda - 1)x^2 + 2(\lambda - 1)x - 2$.
(I) Discuss the monotonicity of function $f(x)$.
(II) When $a=2$, the inequality $f(x) \leq g(x)$ holds for all $x$. Find the minimum integer value of $\lambda$.

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