
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
Three identical cylindrical jars, each with a diameter of 12 cm, are stacked in a triangular formation within a box. Calculate the total height, \( h \), of this arrangement.

[asy]
draw(circle((10,10),12),black+linewidth(1));
draw(circle((34,10),12),black+linewidth(1));
draw(circle((22,32.784),12),black+linewidth(1));
draw((60,0)--(60,45),black+linewidth(1));
draw((59,0)--(61,0),black+linewidth(1));
draw((59,45)--(61,45),black+linewidth(1));
label("$h$",(60,0)--(60,45),E);
[/asy]

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