
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 a quadrant of a circle ${x}^{2}+{y}^{2}=2$ where $x\geqslant 0, y\geqslant 0$, and the graphs of the functions $f(x)={\mathrm{log}}_{2015}x$ and $g(x)={2015}^{x}$ intersect at points $A({x}_{1},{y}_{1})$ and $B({x}_{2},{y}_{2})$, find the value of ${x}_{1}^{2}+{x}_{2}^{2}$.

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