
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 a regular hexagon \(ABCDEF\), points \(M\) and \(K\) are taken on the diagonals \(AC\) and \(CE\) respectively, such that \(AM : AC = CK : CE = n\). Points \(B, M,\) and \(K\) are collinear. Find \(n\).

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