
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 $F\_1$ and $F\_2$ are the left and right foci of the ellipse $\frac{x^2}{36} + \frac{y^2}{27} = 1$, respectively, and $A$ is a point on the ellipse. If $\overrightarrow{OB} = \frac{1}{2}(\overrightarrow{OA} + \overrightarrow{OF\_1})$ and $\overrightarrow{OC} = \frac{1}{2}(\overrightarrow{OA} + \overrightarrow{OF\_2})$, find the value of $(|\overrightarrow{OB}| + |\overrightarrow{OC}|)$.

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