
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
Given that $\left(2x-21\right)\left(3x-7\right)-\left(3x-7\right)\left(x-13\right)$ can be factored as $\left(3x+a\right)\left(x+b\right)$, where $a$ and $b$ are integers.<br/>$(1)$ Find the value of $a+3b$;<br/>$(2)$ Similarly, factorize $x^{2}-3x+2$ in the form of $\left(x+a\right)\left(x+b\right)$.

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