
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
As part of his effort to take over the world, Edward starts producing his own currency. Alex works in the mint and produces 1 counterfeit coin for every 99 real ones. The scale used to weigh the coins is accurate 95% of the time; 5% of all coins minted are sent to a lab for testing. The lab's test is accurate 90% of the time. If the lab says a coin is counterfeit, what is the probability that it really is?

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