
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 $P\left(2a-2,a+5\right)$, solve the following:<br/>$(1)$ If the coordinates of point $Q$ are $\left(4,5\right)$, and the line $PQ$ is parallel to the $y$-axis, then the coordinates of $P$ are ________;<br/>$(2)$ If point $P$ is in the second quadrant and the distance from $P$ to the $x$-axis is equal to the distance from $P$ to the $y$-axis, find the value of ${a^{2023}}+\sqrt[3]{a}$.

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