
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 bike shed, there are bicycles (two wheels), tricycles, and cars (four wheels). The number of bicycles is four times the number of cars. Several students counted the total number of wheels in the shed, but each of them obtained a different count: $235, 236, 237, 238, 239$. Among these, one count is correct. Smart kid, please calculate the number of different combinations of the three types of vehicles that satisfy the given conditions. (For example, if there are 1 bicycle, 2 tricycles, and 3 cars or 3 bicycles, 2 tricycles, and 1 car, it counts as two different combinations).

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