
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

Calculate the force with which water presses on a dam, whose cross-section has the shape of an isosceles trapezoid. The density of water is $\rho=1000\, \mathrm{kg/m^3}$, and acceleration due to gravity $g$ is assumed to be $10\, \mathrm{m/s^2}$.

Hint: The pressure at a depth $x$ is $\rho g x$.

Values:
- $a = 6.9\, \mathrm{m}$ (shorter base of the trapezoid)
- $b = 11.4\, \mathrm{m}$ (longer base of the trapezoid)
- $h = 5.0\, \mathrm{m}$ (height of the trapezoid)

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