
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 $a > 0$, the function $f(x) = -2a\sin(2x + \frac{\pi}{6}) + 2a + b$, where $x \in [0, \frac{\pi}{2}]$, has a range of $[-5, 1]$.
1. Find the values of the constants $a$ and $b$.
2. Let $g(x) = f(x + \frac{\pi}{2})$ and the domain of $g(x)$ be the solution set of the inequality $\log[g(x)] > 0$. Determine the intervals where $g(x)$ is monotonic.

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