
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
On the number line, a moving point $Q$ starts from the origin $O$ and moves back and forth along the number line at a speed of $4$ units per second. The first move is to the right by $1$ unit, the second move is to the left by $2$ units, the third move is to the right by $3$ units, the fourth move is to the left by $4$ units, the fifth move is to the right by $5$ units, and so on. (Reference formula: $1+2+3+4+\cdots +n=\frac{n×(n+1)}{2}$)<br/>$(1)$ After the $8$th move, point $Q$ is at the position of ______ and the total time taken is ______ seconds;<br/>$(2)$ Find the position of point $Q$ after $7$ seconds;<br/>$(3)$ If there is a fixed point $A$ on the number line to the left of the origin $O$, $24$ units away from the origin $O$, can the moving point $Q$ coincide with point $A$ after moving? If yes, how long does it take for the first time to coincide with point $A$? If not, please explain the reason.

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