
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 \(\vec{a} + \vec{b} = 2 \vec{i} - 8 \vec{j}\) and \(-\vec{a} + 2 \vec{b} = -11 \vec{i} + 5 \vec{j}\), find the angle \(\theta\) between \(\vec{a}\) and \(\vec{b}\).

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