
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
A reception hall in the palace of the thirteenth kingdom comprises points on a plane whose coordinates satisfy the condition \(4|x| + 5|y| \leq 20\). How many identical tiles of double-sided parquet, each in the shape of a right triangle with legs 1 and \(5/4\), are required to tile the floor of the hall? Tiling is considered to be done without any gaps, overlaps, and without extending beyond the area.

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