
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 basketball team has $15$ players dressed for a game: $5$ players start the game and $10$ players are available as substitutes. During the game, the coach can make up to $4$ substitutions. A player who leaves the game cannot re-enter, but a substitute who enters can be replaced later. We treat substitutions where the players involved and the orders in which they occur as distinct. Let $n$ be the number of ways the coach can make these substitutions during the game, including the possibility of making no substitutions. Find the remainder when $n$ is divided by $1000$.

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