
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 tosses, you can count the number of occurrences of a tails followed by a heads (denoted as "TH"), a heads followed by a heads (denoted as "HH"), a tails followed by a tails (denoted as "TT"), and a heads followed by a tails (denoted as "HT"). For example, in a sequence of 15 coin tosses resulting in: HH, TT, TH, HH, HT, there are 5 "HH", 3 "HT", 2 "TH", and 4 "TT". How many different result sequences of 15 coin tosses are there where there are exactly 2 "HH", 3 "HT", 4 "TH", and 5 "TT"?

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