
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 \( 3 \vec{a} - 2 \vec{b} = \{-2,0,4\} \), \( \vec{c} = \{-2,1,2\} \), \( \vec{a} \cdot \vec{c} = 2 \), and \( |\vec{b}| = 4 \). Find the angle \(\theta\) between \(\vec{b}\) and \(\vec{c}\).

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