
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
Suppose there is a decision-making system where each member's decisions do not affect each other, and the probability of each member making a correct decision is $p (0 < p < 1)$. The system makes a correct decision when more than half of the members make a correct decision. To make a 5-member decision-making system more reliable than a 3-member system, determine the range of $p$.

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