
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 two points A(1, 0), B(1, $\sqrt{3}$), and O as the origin, point C is in the first quadrant, and $\angle AOC = \frac{\pi}{6}$. Let $\overrightarrow{OC} = 2\overrightarrow{OA} + \lambda\overrightarrow{OB}$, ($\lambda \in \mathbb{R}$), then determine the value of $\lambda$.

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