
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 volleyball team has 18 total players. A fixed set of 6 players starts the game, while the other 12 are available as substitutes. During the game, the coach may make up to 5 substitutions (according to the same rules as in soccer, no reentry, order matters, one at a time). No two substitutions can occur at the same time. Define \( n \) as the number of ways the coach can execute substitutions during the game, including making no substitutions at all. Compute the remainder when \( n \) is divided by $1000$.

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