
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
During a Children's Day promotional event at a shopping mall, customers who spend a minimum of $100 are eligible to participate in a shooting game to win a toy. The rules are as follows: each person can shoot up to 3 times, and if they hit the target, they win and no longer continue shooting; otherwise, they keep shooting until they have used up all 3 attempts. Let $p$ denote the probability that person A hits the target each time, and let $\eta$ denote the number of shooting attempts. If the mathematical expectation $E(\eta) > \frac{7}{4}$, find the range of values for $p$.

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