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

(1) Find the angle $\theta$ between $a$ and $b$;

(2) Find $|a+b|$;

(3) If $\overrightarrow{AB} = a$ and $\overrightarrow{BC} = b$, find the area of $\triangle ABC$.

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