
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
If the straight line $3x-4y+5=0$ intersects with the circle ${x}^{2}+{y}^{2}={r}^{2}\phantom{\rule{0.33em}{0ex}}(r>0)$ at points $A$ and $B$, and $\mathrm{\angle }AOB={120}^{\circ }\phantom{\rule{0.33em}{0ex}}(O$ is the origin of the coordinate system), then $r=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.$

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