
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
At an international event there are  $100$  countries participating, each with its own flag. There are  $10$  distinct flagpoles at the stadium, labelled 1,#2,...,#10 in a row. In how many ways can all the  $100$  flags be hoisted on these  $10$  flagpoles, such that for each  $i$  from  $1$  to  $10$ , the flagpole #i has at least  $i$  flags? (Note that the vertical order of the flagpoles on each flag is important)

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