
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
A structure is constructed using unit cubes where each cube shares at least one full face with another cube. What is the minimum number of cubes needed to build a structure with the front and side views below, where not only do they satisfy the shown views but also have a third height condition where the back view is just a single cube in height?
[asy]
/* Custom Variation of AMC8 2003 #15 Problem */
draw((0,0)--(1,0)--(1,2)--(0,2)--cycle);  // simple rectangle for the front
draw((3,0)--(5,0)--(5,1)--(4,1)--(4,2)--(3,2)--cycle);  // modified shape for the side
draw((6,0)--(7,0)--(7,1)--(6,1)--cycle);  // back view
label(scale(0.8)*"FRONT", (0.5, 0), S);
label(scale(0.8)*"SIDE", (4,0), S);
label(scale(0.8)*"BACK", (6.5,0), S);
[/asy]

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