
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
In a sequence of coin toss results, you can count the number of occurrences where a tail is followed by a head (denoted as "TH"), a head is followed by a head (denoted as "HH"), a tail is followed by a tail (denoted as "TT"), and a head is followed by a tail (denoted as "HT"). For example, in the sequence of 15 coin tosses:

HHTTHHTTHHTHTH

There are 2 occurrences of "TH", 5 occurrences of "HH", 3 occurrences of "HT", and 4 occurrences of "TT". How many different sequences of 15 coin tosses can result in exactly 2 "TH", 3 "HT", 4 "TT", and 5 "HH"?

(From the 4th American Invitational Mathematics Examination)

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