
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
In a new setup, three identical square crates are packed with cylindrical pipes, each with a diameter of $12 \text{ cm}$. Pipes are stacked in a triangular formation in each crate but with heights of the stacks varying. In Crate C, exactly three pipes are stacked such that they touch each other, as shown in the side view diagram. Determine the total height, \( h \), of this stack of \( 3 \) pipes.

\[ \text{Description of Crate C with 3 pipes stacked} \]
\[ \text{[Pipe placement similar to previous problem but with updated dimensions]} \]

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