
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
A biased coin is flipped six times. The probability of obtaining heads exactly twice is the same as obtaining heads exactly three times. Compute the probability that the coin comes up heads exactly four times out of the six flips and express your answer as a sum of numerators and denominators.

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