
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, with 5 starting players and 10 substitutes. During a game, the coach can make up to 5 substitutions. Each substitution involves replacing one of the players currently in the game with one of the substitutes, and no player who leaves the game can reenter. The order of substitutions and the players involved are important. Let $m$ be the number of ways the coach can make substitutions during the game (including the possibility of making no substitutions). Calculate the remainder of $m$ when divided by $1000$.

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