
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
Given point $P(2a-2,a+5)$, solve the following questions:
1. If point $P$ lies on the $x$-axis, find the coordinates of point $P$.
2. If the coordinates of point $Q$ are $(4,5)$ and the line $PQ$ is parallel to the $y$-axis, find the coordinates of point $P$.
3. If point $P$ lies in the second quadrant and the distances from point $P$ to the $x$-axis and $y$-axis are equal, find the value of $a^{2023}+2022$.

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