
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 the graph of a linear function $y_{1}=kx+b$ intersects with the graph of an inverse proportion function $y_{2}=\dfrac{m}{x}$ at point $A(2,2)$ and $B(-1,a)$:
1. Find the expressions of the linear function and the inverse proportion function.
2. Let point $P(h,y_{1})$ and $Q(h,y_{2})$ be points on the graphs of the two functions:
   - Determine the range of $h$ when $y_{1} \gt y_{2}$.
   - If $y_{1}-y_{2}=2$, find the value of $h$.

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