
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 that water exerts 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 the acceleration due to gravity is $g = 10 \, \mathrm{m/s}^2$.

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

Given:
$$
a = 5.1 \, \mathrm{m}, \quad b = 7.8 \, \mathrm{m}, \quad h = 3.0 \, \mathrm{m}
$$

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