
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
In the Cartesian coordinate plane $(xOy)$, let line $y=-x+2$ intersect circle $x^{2}+y^{2}=r^{2}(r > 0)$ at points $A$ and $B$. Let $O$ be the origin, and if there is a point $C$ on the circle such that $\overrightarrow{OC}=\frac{5}{4}\overrightarrow{OA}+\frac{3}{4}\overrightarrow{OB}$, find the value of $r$.

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