
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
Given the conditions that a 15-letter arrangement of 4 D's, 6 E's, and 5 F's has no D's in the first 4 letters, no E's in the next 6 letters, and no F's in the last 5 letters, find the number of valid arrangements.

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