
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 biased coin is flipped six times, the probability of getting heads exactly twice is equal to the probability of getting heads exactly three times. Find the probability that the coin shows heads exactly four times in these six flips, then find $i+j$ where this probability is expressed as $\frac{i}{j}$ in lowest terms.

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