
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
Given the lines $y=3x$, $y=1$, and $x=4$, determine the number of rectangles with sides parallel to the axes and whose vertices have integer coordinates that lie entirely within the region bounded by these lines.

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