
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
Let points $A$, $B$, and $C$ be such that $\frac{AC}{AB} = \frac{BC}{AB} = \frac{1}{3}$. If $B = (2, 10)$ and $C = (5, 4)$, then what is the sum of the coordinates of $A$?

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