
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 SHORT BINGO, a $5\times5$ card has the middle square marked as WILD, with 24 other numbers placed in the remaining squares. Numbers are placed as follows: the first column contains 5 distinct numbers from the set $1-15$, the second column contains 5 distinct numbers from $16-30$, 4 distinct numbers from $31-45$ in the third column (excluding the WILD square in the middle), 5 distinct numbers from $46-60$ in the fourth column, and 5 distinct numbers from $61-75$ in the last column.

Calculate the number of distinct possibilities for the values in the first column of this modified SHORT BINGO card.

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