
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 bag contains $\frac{1}{2}$ white kernels, $\frac{1}{3}$ yellow kernels, and $\frac{1}{6}$ red kernels. Half of the white kernels will pop, two-thirds of the yellow kernels will pop, and one-third of the red kernels will pop. Determine the probability that the kernel selected was white.

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