
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
In triangle $ABC$, median $AF$ from vertex $A$ to side $BC$ is $10$ units and median $BE$ from vertex $B$ to side $AC$ is $15$ units. These medians intersect at right angles at point $G$, the centroid of triangle $ABC$. An altitude from vertex $C$ to line $AB$ is also given as $12$ units. Find the area of triangle $ABC$.
A) 100
B) 120
C) 130
D) 140
E) 150

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