
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 that $|\overrightarrow{OA}|=3$, $|\overrightarrow{OB}|=4$, $\overrightarrow{OA} \cdot \overrightarrow{OB} = 0$, and $\overrightarrow{OC} = \sin^2{\theta} \cdot \overrightarrow{OA} + \cos^2{\theta} \cdot \overrightarrow{OB}$, find the minimum value of $|\overrightarrow{OC}|$ and express $\overrightarrow{OC}$ in terms of $\overrightarrow{OA}$ and $\overrightarrow{OB}$.

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