
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 \(y = h(x)\) is a piecewise function given as follows:
- \(h(x) = -x - 2\) for \(-4 \leq x \leq 0\),
- \(h(x) = \sqrt{9 - (x - 3)^2} - 3\) for \(0 < x \leq 3\),
- \(h(x) = 3(x - 3)\) for \(3 < x \leq 4\).

For certain constants \(p\), \(q\), and \(r\), the function \(j(x)\) is defined by:
\[j(x) = ph(qx) + r.\]
The graph of \(y = j(x)\) is obtained by stretching the graph of \(y = h(x)\) horizontally by a factor of 3 and shifting it downward by 5 units.

Determine the ordered triple \((p, q, r)\).

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