
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 all values of \( p \) such that for every \( q > 0 \), the inequality 
$$\frac{4(2pq^2 + p^2q + 4q^2 + 4pq)}{2p+q} > 3p^2q$$
holds. Express your answer in interval notation in decimal form.

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