
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 parabola $y=x^2-x\cos\theta+2\sin\theta-1$ (where $\theta$ is a parameter).
(1) Find the function relationship $f(\theta)$ between the sum of the squares of the two intercepts on the x-axis and $\theta$;
(2) Find the minimum and maximum values of $f(\theta)$.

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