
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 the trapezoid \( OABC \), where \( \overrightarrow{CB} \parallel \overrightarrow{OA} \) and \( |\overrightarrow{CB}| = \frac{1}{2} |\overrightarrow{OA}| \). Let \( \overrightarrow{OA} = \vec{a} \) and \( \overrightarrow{OC} = \vec{b} \). Determine \( \overrightarrow{AB} = \) .

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