
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 certain school is conducting fixed-point shooting training. Three students, A, B, and C, are shooting at fixed positions. The probabilities of them making a shot are $\frac{1}{2}$, $\frac{2}{3}$, and $p$, respectively. It is known that the shooting of each person does not affect the others. If these three students each take one shot, the probability of at least one person making a shot is $\frac{7}{8}$. Find the value of $p$.

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