
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
Two people, $A$ and $B$, form the "Dragon Team" to participate in a knowledge competition. In each round, $A$ and $B$ each answer a question. It is known that the probability of $A$ answering correctly in each round is $\frac{1}{3}$, and the probability of $B$ answering correctly is $p$. In each round of the activity, the answers of $A$ and $B$ do not affect each other, and the results of each round are also independent. If the probability of the "Dragon Team" answering one riddle correctly in the first round is $\frac{1}{2}$. Find the value of $p$. Find the probability that the "Dragon Team" answers one question incorrectly in two rounds.

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