
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
Zhenya took a $3 \times 3$ board and placed a column of blue and red cubes on each cell. Then he drew a diagram of the resulting arrangement: he wrote down the number of cubes of both colors in each column (the order of the cubes is unknown).

What is the maximum number of blue cubes Zhenya can see if he looks at the construction from the front? (For example, if a column of 8 cubes stands behind a column of 5, he will see all 5 cubes of the front column and only 3 upper cubes of the rear column.)

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