
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
John has 20 coins consisting of two types of rare coins. He finds out that 7 coins of the first type are worth $21, and 5 coins of the second type are worth $30 in total. Assuming the coins of each type have the same value, how much is his entire collection worth if he has 12 coins of the first type and 8 of the second type?

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