
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
In a game, there are several tiles of different colors and scores. Two white tiles are equal to three yellow tiles, a yellow tile equals  $5$  red chips,  $3$  red tile are equal to  $ 8$  black tiles, and a black tile is worth  $15$ .
i) Find the values ​​of all the tiles.
ii) Determine in how many ways the tiles can be chosen so that their scores add up to  $560$  and there are no more than five tiles of the same color.

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