
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
Construction workers need to lay the floor of a small house with small square tiles. The client prefers an arrangement where there are more red tiles. For options with an equal number of red tiles, the preferred one has more orange tiles; and generally, the client's color preferences are: red, orange, yellow, green, blue, indigo. However, his wife has the exact opposite preferences:

- The number of indigo tiles should be at least equal to the combined number of red, orange, yellow, green, and blue tiles.
- The number of blue tiles should be at least equal to the combined number of red, orange, yellow, and green tiles.
- The number of green tiles should be at least equal to the combined number of red, orange, and yellow tiles.
- The number of yellow tiles should be at least equal to the combined number of red and orange tiles.
- The number of orange tiles should be at least equal to the number of red tiles.

A total of 100 tiles is required for the floor.

How many green tiles are needed if using the client's most preferred option that also meets the conditions of his wife?

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