
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
If \(\left(\frac{1 \times 2 \times 4+2 \times 4 \times 8+3 \times 6 \times 12+\cdots+1999 \times 3998 \times 7996}{1^{3}+2^{3}+3^{3}+\cdots+1999^{3}}\right)^{\frac{1}{3}}=P\), find the value of \(P\).

If \((x-P)(x-2Q)-1=0\) has two integral roots, find the value of \(Q\).

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