
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
Let  $N$  be the number of consecutive 0's at the right end of the decimal representation of the product  $1!\times2!\times3!\times4!\cdots99!\times100!.$   Find the remainder when  $N$  is divided by 1000.

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