
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
The regular hexagon \(ABCDEF\) has diagonals \(AC\) and \(CE\). The internal points \(M\) and \(N\) divide these diagonals such that \(AM: AC = CN: CE = r\). Determine \(r\) if it is known that points \(B\), \(M\), and \(N\) are collinear.

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