
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
Find the solution that satisfies the system of inequalities:

$$
\left\{\begin{array}{c}
19p < 10, \\
p > 0.5
\end{array}\right., \text{ resulting in } \frac{1}{2} < p < \frac{10}{19}
$$

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