
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 $|\overrightarrow{a}|=4$, $|\overrightarrow{b}|=3$, and $(2\overrightarrow{a}-3\overrightarrow{b}) \cdot (2\overrightarrow{a}+\overrightarrow{b})=61$.

(I) Find the angle $\theta$ between $\overrightarrow{a}$ and $\overrightarrow{b}$;

(II) If we set $\overrightarrow{OA}=\overrightarrow{a}$ and $\overrightarrow{OB}=\overrightarrow{b}$, find the length of the two diagonals of the parallelogram where $OA$ and $OB$ are adjacent sides.

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