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

Note: The pressure at a depth $x$ is given by $\rho g x$.

$$
a=6.3 \mathrm{m}, b=10.2 \mathrm{m}, h=4.0 \mathrm{m}
$$

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