
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 a certain biased coin is flipped seven times, the probability of getting heads exactly twice is the same as the probability of getting heads exactly thrice. Given that the probability of getting heads in one flip is not zero, find $\frac{i}{j}$ in lowest terms, where $i+j$ is the probability that the coin comes up heads in exactly four out of the seven flips.

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