
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
Parallelogram \(EFGH\) with \(E(3,4)\), \(F(5,7)\), \(G(7,4)\), and \(H(5,1)\) is reflected across the \(x\)-axis to \(E'F'G'H'\) and then \(E'F'G'H'\) is reflected across the line \(y=x-1\) to \(E''F''G''H''\). This is done such that \(H'\) is the image of \(H\), and \(H''\) is the image of \(H'\). What is the ordered pair of \(H''\) in the coordinate plane?

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