
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
**9.** Find all pairs of linear polynomials  $f(x)$ ,  $g(x)$  with integer coefficients for which there exist two polynomials  $u(x)$ ,  $v(x)$  with integer coefficients such that  $f(x)u(x)+g(x)v(x)=1$ . **(A. 8)**

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