
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
Let $A B C D E F$ be a regular hexagon, with $M$ a point on the diagonal $A C$ and $N$ a point on $C E$ such that

$$
\frac{A M}{A C}=\frac{C N}{C E}=r
$$

What can be said about $r$ if $B, M,$ and $N$ are collinear?

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