
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
Five identical cylindrical pipes are stacked in a crate with two on the bottom and three resting on top of the first two. Each pipe has a diameter of $12\text{ cm}.$ Determine the height, $h,$ of this pile of $5$ pipes as shown below.

[asy]
draw(circle((10,10),12),black+linewidth(1));
draw(circle((30,10),12),black+linewidth(1));
draw(circle((20,30.62),12),black+linewidth(1));
draw(circle((8,30.62),12),black+linewidth(1));
draw(circle((32,30.62),12),black+linewidth(1));
draw((50,0)--(50,50.74),black+linewidth(1));
draw((49,0)--(51,0),black+linewidth(1));
draw((49,50.74)--(51,50.74),black+linewidth(1));
label("$h$",(50,0)--(50,50.74),E);
[/asy]

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