
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 $f(x)=\cos^2x+a\sin x+2a-1$, where $a\in \mathbb{R}$.
1. When $a=1$, find the maximum and minimum values of the function and the corresponding values of $x$.
2. If for any $x$ in the interval $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$, it always holds that $f(x) \leqslant 5$, find the range of values for $a$.

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