
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
From the numbers $1$, $2$, $3$, $4$, $5$, select $2$ numbers to form a two-digit number without repeating digits. Please calculate:

$(1)$ The probability that this two-digit number is a multiple of $5$;

$(2)$ The probability that this two-digit number is an even number;

$(3)$ If the problem is changed to "Select $3$ numbers from $1$, $2$, $3$, $4$, $5$ to form a three-digit number without repeating digits", then calculate the probability that this three-digit number is greater than $234$.

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