
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
Line segment $AB=100cm$, $MN=40cm$ (point $B$ is to the right of point $A$, point $M$ is to the right of point $N$) move at a constant speed on a straight line. To determine the position of the points, we represent this straight line with a number line, and define the positive direction as to the right, with the origin $O$ at $0cm$. The convention is as follows: a positive position indicates the point is to the right of zero centimeters; a negative position indicates the point is to the left of zero centimeters, and a position of zero indicates the point is at zero centimeters. The table below shows some data. When the overlapping part of line segment $AB$ and $MN$ is $32$, $x=\_\_\_\_\_\_$.

| Time $(s)$ | $0$ | $3$ | $5$ | $x$ |
|------------|-----|-----|-----|-----|
| Position of point $A$ $(cm)$ | $120$ | $-30$ | $-$ | $-$ |
| Position of point $N$ $(cm)$ | $-$ | $60$ | $120$ | $-$ |

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