
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
We construct a channel from three boards of equal width. The side walls form an angle of $x$ with the base board. What value of the angle $x$ will make the cross-sectional area (and thus the volume) of the channel (which forms the shape of an isosceles trapezoid) the largest possible?

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