
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
Compute the smallest integer  $n\geq 4$  such that  $\textstyle\binom n4$  ends in  $4$  or more zeroes (i.e. the rightmost four digits of  $\textstyle\binom n4$  are  $0000$ ).

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