
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 $\rho=1000 \ \text{kg/m}^3$ and the acceleration due to gravity $g$ is $10 \ \text{m/s}^2$.

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

Given:
- \( a = 7.2 \ \text{m} \)
- \( b = 12.0 \ \text{m} \)
- \( h = 5.0 \ \text{m} \)

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