
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
At the mill dikes, sloped channels with cross-sections in the shape of right-angled parallelograms are usually used for drainage of excess water. For such a channel, water enters the upper end at a speed of $1.4 \frac{\mathrm{m}}{\text { sec }}$ and flows through it with a thickness of $0.4 \mathrm{~m}$. The channel has a length of $10 \mathrm{~m}$, a constant width of $3.5 \mathrm{~m}$, and an inclination angle of $12^{\circ}$. In what thickness does the water flow at the lower end of the channel? How wide should this channel have been built so that the water flows as thickly at the lower end as at the upper end?

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