
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 $f(x) = \log_{\frac{1}{2}}(x+a)$, $g(x) = x^2 + 4x - 2$, and the function $h(x) = \begin{cases} f(x), & \text{if } f(x) \geq g(x) \\ g(x), & \text{if } f(x) < g(x) \end{cases}$, find the value of $a$ when the minimum value of the function $h(x)$ is -2.

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