
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
A square has vertices at $(0,0),(1,0),(1,1)$ and $(0,1)$. Graphs of the following equations are drawn on the same set of axes as the square.
$$
x^{2}+y^{2}=1, \quad y=x+1, \quad y=-x^{2}+1, \quad y=x, \quad y=\frac{1}{x}
$$

How many of the graphs pass through exactly two of the vertices of the square?
A 1
B 2
C 3
D 4
E 5

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