
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]


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Modify the constants in the problem: Let's alter the probability such that when a coin is flipped four times, the probability of having exactly two heads is $\frac{1}{12}$. Given that the coin's probability of landing on heads is less than $\frac{1}{2}$, find the probability that the coin lands on heads.
**A)** $\frac{12 + \sqrt{96 + 48\sqrt{2}}}{24}$
**B)** $\frac{12 - \sqrt{96 + 48\sqrt{2}}}{24}$
**C)** $\frac{12 + \sqrt{48 - 12\sqrt{2}}}{24}$
**D)** $\frac{12 - \sqrt{48 - 12\sqrt{2}}}{24}$
**E)** $\frac{12 - \sqrt{96 - 48\sqrt{2}}}{24}$

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