
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
In a modified version of SHORT BINGO, a $5\times5$ card is still used, with the middle square marked as WILD. For diversifying the gameplay, the numbering range is altered. The first column now contains any 5 distinct numbers from the set $1-15$, the second from $16-30$, the third from $31-45$ (excluding the WILD in the middle), the fourth from $46-60$, and the last from $61-75$.

Calculate how many distinct possibilities there are for the values in the first column of this modified SHORT BINGO card. Remember, the order of numbers matters, so permutations of the same set are counted as distinct.

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