
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 $P\left(2a-3,a+6\right)$, solve the following questions:<br/>$(1)$ If point $P$ lies on the $x$-axis, find the coordinates of point $P$;<br/>$(2)$ 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 $a^{2003}+2024$.

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