
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 available players. A fixed set of 5 players starts the game, while the other 10 are available as substitutes. During the game, the coach may make as many as 4 substitutions, where any one of the 5 players in the game is replaced by one of the substitutes. No player removed from the game may reenter the game, although a substitute entering the game may be replaced later. No two substitutions can happen at the same time. The players involved and the order of the substitutions matter. Calculate the number of ways the coach can make substitutions during the game, including the possibility of making no substitutions, and find the remainder when this number is divided by 1000.

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