
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 pushes against a dam, whose cross-section has the shape of an isosceles trapezoid. The density of water is $\rho=1000 \, \text{kg/m}^3$, and the acceleration due to gravity is $g=10 \, \text{m/s}^2$.

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

Given data:
- $a = 5.4 \, \text{m}$ (top length of the trapezoid)
- $b = 8.4 \, \text{m}$ (bottom length of the trapezoid)
- $h = 3.0 \, \text{m}$ (height of the trapezoid)



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