
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
The polynomial  $R(x)$  is the remainder upon dividing  $x^{2007}$  by  $x^2-5x+6$ .  $R(0)$  can be expressed as  $ab(a^c-b^c)$ . Find  $a+c-b$ .

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