
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
Adriana likes to paint geometric shapes. She painted the front of a wall of her house as follows:

a) The wall is rectangular, with a height of $1 \mathrm{~m}$ and a width of $4 \mathrm{~m}$. The four interior squares each have a side length of $1 \mathrm{~m}$. What is the area of the region she painted in gray?

b) Adriana enjoyed the activity and decided to paint the front of another rectangular wall in a similar way. This wall has a height of $1 \mathrm{~m}$ and a width of $32 \mathrm{~m}$. She divides this rectangular wall into 32 squares, each with a side length of $1 \mathrm{~m}$, and then draws a diagonal. Next, she paints the regions alternately, as in the previous wall. Below is the representation of the leftmost part of the wall:

What area of the wall is painted gray? (The total area painted gray, not just the part of the wall shown above).

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