
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, and the other 11 are available as substitutes. During the game, the coach may make as many as 4 substitutions, where any one of the 11 players in the game is replaced by one of the substitutes. No player removed from the game may reenter, although a substitute entering the game may be replaced later. No two substitutions can happen at the same time. Players involved and the order of substitutions matter. Calculate the number of ways the coach can make substitutions during the game (including the possibility of making no substitutions). Finally, find the remainder when this number is divided by 1000.

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