
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
On the edge \(AD\) and the diagonal \(A_1C\) of the parallelepiped \(ABCDA_1B_1C_1D_1\), points \(M\) and \(N\) are taken respectively, such that the line \(MN\) is parallel to the plane \(BDC_1\) and \(AM:AD = 1:5\). Find the ratio \(CN:CA_1\).

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