
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 such linear functions \( P(x) \) and \( Q(x) \) that the equality \( P(x)\left(2 x^{3}-7 x^{2}+7 x-2\right) + Q(x)\left(2 x^{3}+x^{2}+x-1\right) = 2 x-1 \) holds.

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