
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
Every day, Xiaoming goes to school along a flat road \(AB\), an uphill road \(BC\), and a downhill road \(CD\) (as shown in the diagram). Given that \(AB : BC : CD = 1 : 2 : 1\) and that Xiaoming's speeds on flat, uphill, and downhill roads are in the ratio 3 : 2 : 4, respectively, find the ratio of the time Xiaoming takes to go to school to the time he takes to come home.

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