
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 \( n \) for which, for any two polynomials \( P(x) \) and \( Q(x) \) of degree \( n \), there exist monomials \( a x^{k} \) and \( b x^{l} \) \((0 \leq k \leq n, 0 \leq l \leq n)\) such that the graphs of the polynomials \( P(x) + a x^{k} \) and \( Q(x) + b x^{l} \) will not have common points.

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