
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
Aladdin has 10 bags of coins, where each bag contains only real coins or only fake coins. Each real coin weighs $10 \mathrm{~g}$ and each fake coin weighs $9 \mathrm{~g}$.

(a) Suppose each bag contains exactly 10 coins and only one of the bags contains fake coins. Using a balance and making only one weighing, how should Aladdin proceed to identify which bag contains the fake coins?

(b) Suppose the bags are full of coins and Aladdin does not know how many of these bags contain fake coins. How can he identify the bags with fake coins using only one weighing?

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