
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 $A=5\sqrt{2x+1}$, $B=3\sqrt{x+3}$, $C=\sqrt{10x+3y}$, where $A$ and $B$ are the simplest quadratic surds, and $A+B=C$, find the value of $\sqrt{2y-x^2}$.

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