
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. If the probability of getting heads exactly twice is equal to the probability of getting heads exactly three times in these flips, find the value of $i+j$ where $\frac{i}{j}$, in lowest terms, is the probability that the coin comes up heads exactly 4 out of 6 flips.

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