
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 $a$ and $b$ with magnitudes $|a|=4$ and $|b|=2$.

(1) If the angle between $a$ and $b$ is $120^{\circ}$, find $|3a-4b|$.

(2) If $|a+b|=2\sqrt{3}$, find the angle $θ$ between $a$ and $b$.

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