
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
Xiao Liang found that the positive integer ■ was contaminated when solving the one-variable linear equation about $x$: $\frac{3x-1}{2}+$■$=3$.

$(1)$ Xiao Liang guessed that ■ was $5$, then the solution of the equation is $x=$______;

$(2)$ If the teacher tells Xiao Liang that the solution of this equation is a positive integer, then what is the contaminated positive integer?

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