
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
Point $A$ lies on segment $BC$ (excluding the endpoints), $O$ is a point outside the line $BC$, and satisfies $\overrightarrow{OA}-a\overrightarrow{OB}-2b\overrightarrow{OC}=\overrightarrow 0$. Find the minimum value of $\frac{2}{{3a+4b}}+\frac{1}{{a+3b}}$.

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