
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 graph of \( y = h(x) \) described as follows:
- For \( x \geq -5 \) and \( x \leq 0 \), \( y = -3 - x \).
- For \( x \geq 0 \) and \( x \leq 3 \), \( y = \sqrt{9 - (x-3)^2} - 3 \).
- For \( x \geq 3 \) and \( x \leq 5 \), \( y = 3(x-3) \).

The graph of \( y = j(x) \) is a transformation of \( y = h(x) \). Determine \( j(x) \) in terms of \( h(x) \) if \( j(x) \) is the result of first reflecting \( h(x) \) across the y-axis and then shifting it right by 5 units.

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