
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 the diagram, \( \triangle ABC \) is right-angled at \( A \) with \( AB = 3 \) and \( AC = 3\sqrt{3} \). Altitude \( AD \) intersects median \( BE \) at \( G \). Calculate the length of \( AG \).

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