
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 the circle $C: x^2+y^2=4$ ($x\geq0, y\geq0$) and the graphs of the functions $f(x)=\log_{2}x$, $g(x)=2^x$ intersect at points $A(x_1,y_1)$, $B(x_2,y_2)$, calculate the value of $x_1^2+x_2^2$.

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