
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
A soccer team has $22$ available players. A fixed set of $11$ players starts the game, while the other $11$ are available as substitutes. During the game, the coach may make as many as $4$ substitutions. As before, each substitution involves replacing one of the players in the game with a substitute, and no player removed from the game may reenter. No two substitutions can happen at the same time, and the players involved as well as the order of substitutions matter. Let $n$ be the number of ways the coach can potentially make substitutions during the game (including the possibility of making no substitutions). Find $n$ modulo $1000$.

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