
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 $23$ players for a game: $11$ start the game, and $12$ are available as substitutes. During the game, the coach may make as many as $4$ substitutions. Each substitution involves one of the current players being replaced by one of the substitutes, with no player reentering once taken off. The players and order of substitutions are important. Let $n$ be the number of ways the coach can execute these substitutions, including the possibility of making no substitutions at all. Calculate $n$ modulo $1000$.

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