
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 $a$ and $b$ be constants, $f(x) = (a - 3) \sin x + b$, and $g(x) = a + b \cos x$, where $f(x)$ is an even function.
1. Find the value of $a$.
2. If the minimum value of $g(x)$ is $-1$ and $\sin b > 0$, find the value of $b$.

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