
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 rectangular coordinate system, the angle $\theta$ satisfies $\sin\frac{\theta}{2}=-\frac{4}{5}$ and $\cos\frac{\theta}{2}=\frac{3}{5}$. Given $\overrightarrow{OA}=(-1,0)$, let point $B$ be a moving point on the terminal side of angle $\theta$. Find the minimum value of $|\overrightarrow{OA}-\overrightarrow{OB}|$.

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