
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 $ABC$, the medians $\overline{AD}$ and $\overline{BE}$ have lengths $24$ and $30$, respectively, and $AC=30$. Extend $\overline{BE}$ to intersect the circumcircle of $ABC$ at $G$. If $D$ is the midpoint of $AC$, and point $H$ on $AB$ is such that $AH = (1/3) AB$, find the area of triangle $AGB$, given the tangent from $D$ to the circumcircle is $15$.

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