
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
Let the set of functions be $P=\{f(x)=\log_{2}(x+a)+b|a=-\frac{1}{2},0,\frac{1}{2},1\}$; $b=-1,0,1\}$, and the set of points on the plane be $Q=\{(x,y)|x=-\frac{1}{2},0,\frac{1}{2},1\}; y=-1,0,1\}$. Then, in the same Cartesian coordinate system, the number of functions in $P$ whose graphs exactly pass through two points in $Q$ is ______.

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