
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 defined in parts as follows:
1. For \(x \geq -4\) and \(x \leq 1\), \(y = 1 - x\).
2. For \(x \geq 1\) and \(x \leq 3\), \(y = \sqrt{4 - (x - 3)^2} + 1\).
3. For \(x \geq 3\) and \(x \leq 4\), \(y = 2(x - 3) + 1\).

The graph of \(y = j(x)\) is derived from the graph of \(y = h(x)\). First, the graph of \(y = h(x)\) is reflected over the y-axis and then shifted 6 units to the right. What is \(j(x)\) in terms of \(h(x)\)?

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