
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 that $| \vec{OA} | = 1$, $| \vec{OB} | = m$, and $\angle AOB = \frac{3}{4} \pi$, point $C$ lies within $\angle AOB$ and $\vec{OA} \cdot \vec{OC} = 0$. If $\vec{OC} = 2\lambda \vec{OA} + \lambda \vec{OB}$ ($\lambda \neq 0$), then find the value of $m$.

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