
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 MODIFIED SHORT BINGO, a $5\times5$ card is filled by marking the middle square as WILD. Modify the assignment of numbers such that the first column consists of 5 distinct numbers from the set $10-25$. The rest of the squares are filled with numbers as follows: 5 distinct numbers from $26-35$ in the second column, 4 distinct numbers $36-45$ in the third column (skipping the WILD square), 5 distinct numbers from $46-55$ in the fourth column, and 5 distinct numbers from $56-65$ in the fifth column. 

How many distinct possibilities are there for the values in the first column of a MODIFIED SHORT BINGO card, where the order of the numbers matters?

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