
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
An amount not exceeding 100,000 P is composed of 5 P coins. If these coins are grouped in sets of 12, 18, or 45, there are always 3 coins left. However, if they are grouped in sets of 11, there is no remainder.

What are the possible amounts that meet these conditions, and how many 5 P coins does such an amount consist of?

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