
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 fair coin is tossed 5 times. The probability of getting exactly one heads is non-zero and is equal to the probability of getting exactly two heads. Let the simplified fraction \(\frac{i}{j}\) represent the probability of getting exactly 3 heads out of 5 tosses. Find the value of \(i + j\).

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