
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 vectors $\overrightarrow{a} = (1,3)$, $\overrightarrow{b} = (m, 2)$, $\overrightarrow{c} = (3,4)$, and that $(\overrightarrow{a} - 3\overrightarrow{b})$ is orthogonal to $\overrightarrow{c}$.

(I) Find the real number $m$.  
(II) Find the angle $\theta$ between vectors $\overrightarrow{a}$ and $\overrightarrow{b}$.

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