
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 $BM$ at point $G$. Determine the length of segment $AG$. Assume point $B$ is opposite the right angle, and $M$ is the midpoint of side $BC$.

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