
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
The graph of $y = f(x)$ is defined piecewise as follows:
$$
f(x) = \begin{cases} 
2x & \text{if } -3 \leq x < -1, \\
-x^2 + 2 & \text{if } -1 \leq x \leq 1, \\
x-1 & \text{if } 1 < x \leq 3.
\end{cases}
$$
Given constants $p$, $q$, and $r$, the function $h(x)$ is defined by
$$h(x) = p f(qx) + r.$$
The graph of $y = h(x)$ results from transforming the graph of $y = f(x)$ as indicated by the parameters $p$, $q$, and $r$. If the graph of $y = h(x)$ is a horizontal stretch by a factor of 3, a vertical stretch by a factor of 2, and a vertical shift downward by 5 units, determine the ordered triple $(p, q, r)$.

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