
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 Vila Par, all the truth coins weigh an even quantity of grams and the false coins weigh an odd quantity of grams. The eletronic device only gives the parity of the weight of a set of coins. If there are  $2020$  truth coins and  $2$  false coins, detemine the least  $k$ , such that, there exists a strategy that allows to identify the two false coins using the eletronic device, at most,  $k$  times.

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