
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 pressure force $P$ exerted by water on a vertically submerged plate in the shape of a triangle $ABC$ with a base $AC = b$ and height $BD = h$, assuming the vertex $B$ of the triangle lies on the free surface of the liquid and the base $AC$ is parallel to it.

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