
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]


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The graph of $h(x)$ is to be derived from the graph of $y = f(x)$, described below. Determine $h(x)$ in terms of $f(x)$. Suppose $f(x)$ is given as:
- $f(x) = -2 - x$ for $x$ in $[-3, 0]$
- $f(x) = \sqrt{4 - (x - 2)^2} - 2$ for $x$ in $[0, 2]$
- $f(x) = 2(x - 2)$ for $x$ in $[2, 3]$

The graph of $h(x)$ is the graph of $f(x)$ reflected over the x-axis and then shifted left by 6 units. What is $h(x)$ in terms of $f(x)$?

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