
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
Find the length of the chord $\left| AB \right|$ where the line $ax+by+c=0$ intersects the circle ${{x}^{2}}+{{y}^{2}}=1$ at two distinct points $A$ and $B$. If $\overrightarrow{OA} \cdot \overrightarrow{OB}=-\dfrac{1}{2}$, where $O$ is the origin of the coordinate system.

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