
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 point \((2, 2, 2)\) is first reflected through the \(xz\)-plane, then rotated \(180^\circ\) about the \(x\)-axis, followed by a reflection through the \(yz\)-plane, and finally translated by \( \vec{v} = (1, -1, 0) \). Find the coordinates of the resulting point.

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