
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  $f$ ,  $g$ ,  $h$ , and  $k$  are functions and  $a$  and  $b$  are numbers such that  $f(x)=(x-1)g(x)+3=(x+1)h(x)+1=(x^2-1)k(x)+ax+b$  for all  $x$ , determine the values of  $a$  and  $b$ .

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