
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
A certain middle school surveyed some students on their "favorite ball sports" and collected and organized the data into a frequency distribution table (partial) as follows:

| Item | Table Tennis | Badminton | Basketball | Soccer |
|------|--------------|-----------|------------|--------|
| Frequency | $40$ | $25$ | $m$ | $n$ |
| Percentage | $40\%$ | | $25\%$ | $n$ |

Find the value of $mn$.

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