
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
Consider the function $f(x) = -2m + 2m\sin(x+ \frac{3\pi}{2}) - 2\cos^2(x - \frac{\pi}{2}) + 1$, where $x \in \left[-\frac{\pi}{2}, 0\right]$ and its minimum value is denoted as $h(m)$.
1. Find $h(m)$.
2. If $h(m) = \frac{1}{2}$, determine the value of $m$ and the maximum value of $f(x)$ under this condition.

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