
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
What are all values of $p$ such that for every $q>0$, the following inequality holds true:
$$\frac{5(pq^2 + 2p^2q + 4q^2 + 4pq)}{p + 2q} > 3p^2q?$$
Express your answer in interval notation.

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