
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 Cartesian coordinate system with origin O, points A(3, 1) and B(-1, 3), and point C satisfying $\overrightarrow{OC} = \alpha\overrightarrow{OA} + \beta\overrightarrow{OB}$, where $\alpha, \beta \in \mathbb{R}$ and $\alpha + \beta = 1$, find the equation of the trajectory of point C.

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