
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
When flipping a coin, if we denote heads as $Z$ and tails as $F$, then a sequence of coin flips can be represented as a sequence composed of $Z$ and $F$. We can count the occurrences of heads followed by tails $(F Z)$, heads followed by heads $(Z Z)$, etc. For example, the sequence
\[ ZZFFZZZZFZZFFFF \]
is the result of flipping a coin 15 times. In this sequence, there are 5 occurrences of $ZZ$, 3 occurrences of $ZF$, 2 occurrences of $FZ$, and 4 occurrences of $FF$. How many sequences of 15 coin flips have exactly 2 occurrences of $ZZ$, 3 occurrences of $ZF$, 4 occurrences of $FZ$, and 5 occurrences of $FF$?

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