
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
What shape should a homogeneous vertical column with a circular cross-section have, such that the pressure from the load $P$ it supports and its own weight per unit area of the horizontal cross-section is the same everywhere? (Column of equal pressure). The specific weight of the material of the column is $\delta$, and the radius of its upper base is $r$.

Then, find the radii of the upper and lower bases of a bridge pier so that the pressure in any of its horizontal cross-sections is $3000 \kappa \Gamma / \text{m}^2$, given the specific weight of the pier material is 2.5, its height is $12 \text{m}$, and the load it supports is $90000 \kappa \Gamma$.

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