
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
Let $f(x) = a^2x^2 - (a^2 - b^2)x - 4c^2$, where $a$, $b$, and $c$ are the lengths of the sides opposite to angles $A$, $B$, and $C$ in triangle $ABC$, respectively. If $f(2) = 0$, then the range of possible values for angle $C$ is ______.

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