
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
Consider the $9 \times 9$ board shown below. The rows are numbered from 1 to 9.

We color the squares in the odd-numbered rows of the board with blue and white alternately, starting with blue. We color the squares in the even-numbered rows of the board with gray and red alternately, starting with gray.

(a) How many squares were painted with each color?

(b) What is the maximum number of pieces of the following form

| $\square \square$ that can |
| :--- | :--- |

be placed on this board without overlapping?

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