
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
The graph of the equation $10x + 270y = 2700$ is drawn on graph paper where each square represents one unit in each direction. A second line defined by $x + y = 10$ also passes through the graph. How many of the $1$ by $1$ graph paper squares have interiors lying entirely below both graphs and entirely in the first quadrant?

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