
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
Using the six digits $0$, $1$, $2$, $3$, $4$, $5$, form integers without repeating any digit. Determine how many such integers satisfy the following conditions:

$(1)$ How many four-digit even numbers can be formed?

$(2)$ How many five-digit numbers that are multiples of $5$ and have no repeated digits can be formed?

$(3)$ How many four-digit numbers greater than $1325$ and with no repeated digits can be formed?

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