
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
When the polynomial $x^5 - 4x^4 + 12x^3 - 14x^2 + 8x + 5$ is divided by $x^2 - 3x + m$, the remainder is $2x + b$. Find the ordered pair $(m, b)$.

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