
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 soccer team has 23 players in total. 12 players start the game, while the remaining 11 are available as substitutes. The coach is allowed to make up to 5 substitutions during the game. Any one of the players in the game can be replaced by one of the substitutes, but substituting players cannot return to the game after being removed. The order of substitutions and players involved is considered in calculating the number of possible substitutions. 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 when $m$ is divided by $100$.

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