
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 diagonals  $AC$  and  $CE$  of the regular hexagon  $ABCDEF$  are divided by inner points  $M$  and  $N$  respectively, so that \[ {AM\over AC}={CN\over CE}=r. \] Determine  $r$  if  $B,M$  and  $N$  are collinear.

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