
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 $f(x) = x^2 - (a-1)x - a^2$  
(1) If $a=3$, $x \in [0, 2]$, find the maximum and minimum values of $f(x)$.  
(2) If $a < 0$, the solution set of the inequality $\sin^2x + a\cos x + a^2 \geq 1 + \cos x$ is $\mathbb{R}$. Find the range of $a$.

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