
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 $h(x)$ formed by modifying the graph of the function $y = f(x)$ defined by the following piecewise function:
- $f(x) = -2 - x$ for $-3 \leq x \leq 0$,
- $f(x) = \sqrt{4 - (x - 2)^2} - 2$ for $0 \leq x \leq 2$, 
- $f(x) = 2(x - 2)$ for $2 \leq x \leq 3$.

The graph of $y = h(x)$ is obtained by compressing the graph of $y = f(x)$ horizontally by a factor of 1/3, reflecting it across the y-axis, and then shifting it upwards by 3 units. Given the transformation, $h(x) = -f(3x) + 3$, find the triple $(a, b, c)$.

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