
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 $33$ available players; $11$ start the game, and the remaining $22$ are ready as substitutes. During a game, the coach can make up to $5$ substitutions, with any one of the starting players being replaced by one of the substitutes. No player removed from the game may return, but a substitute who has come into the game can be replaced later. Let $n$ be the number of possible substitution combinations the coach can execute during the game (including the possibility of making no substitutions). Determine the remainder when $n$ is divided by $1000$.

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