
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
Let the distribution of the random variable $X$ be as shown in the table below:

| $X$ | $1$ | $2$ | $3$ | $4$ |
|-----|-----|-----|-----|-----|
| $P$ | $m$ | $\frac{1}{4}$ | $\frac{1}{4}$ | $\frac{1}{3}$ |

Find $P\left(|X-2|=1\right)=\_\_\_\_\_\_$.

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