
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
Let $M$ denote the number of permutations of the 15-character string $DDDDDEEEEEFFFFF$ such that:
- None of the first five letters is a $D$.
- None of the next five letters is an $E$.
- None of the last five letters is an $F$.
Find the remainder when $M$ is divided by $1000$.

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