
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
A point $(2,2,2)$ undergoes the following transformations:
1. Reflected through the $yz$-plane.
2. Rotated $90^\circ$ about the $z$-axis.
3. Reflected through the $xy$-plane.
4. Rotated $180^\circ$ about the $x$-axis.
5. Reflected through the $xz$-plane.
6. Rotated $90^\circ$ about the $z$-axis.

Find the coordinates of the point after these transformations.

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