
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 \( f(x) = \sin^4 x \),
1. Let \( g(x) = f(x) + f\left(\frac{\pi}{2} - x\right) \). Find the maximum and minimum values of \( g(x) \) in the interval \(\left[\frac{\pi}{6}, \frac{3\pi}{8}\right]\).
2. Find the value of \(\sum_{k=1}^{89} f\left(\frac{k\pi}{180}\right)\).

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