
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
In general, the equation $\frac{a}{2} + \frac{b}{3} = \frac{a+b}{2+3}$ does not hold true. However, there are some numbers that can satisfy it, for example, $a=b=0$. We call a pair of numbers $(a, b)$ that satisfies $\frac{a}{2} + \frac{b}{3} = \frac{a+b}{2+3}$ a "companion pair," denoted as $(a, b)$.
(1) If $(1, b)$ is a "companion pair," find the value of $b$;
(2) Provide an example of a "companion pair" $(a, b)$ where $a\neq 0$, and $a\neq 1$;
(3) If $(m, n)$ is a "companion pair," calculate the value of the algebraic expression $m - \frac{22}{3}n - [4m - 2(3n - 1)]$.

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