
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 a laboratory, there are 120 visually indistinguishable test tubes on a shelf. Of these, 118 contain a neutral substance, one contains poison, and one contains an antidote. The test tubes have been randomly shuffled, and it is necessary to identify the test tube with the poison and the one with the antidote. For this, you can use the services of an external testing laboratory, where you can simultaneously send several mixtures of liquids from any number of test tubes (with one drop from each test tube). For each mixture, the laboratory provides the result: \$+1\$ if the mixture contains poison and no antidote; \$-1\$ if the mixture contains the antidote but no poison; and 0 in all other cases. Is it possible, by preparing 19 such mixtures and sending them to the laboratory in one batch, to guarantee the identification of the test tube with the poison and the one with the antidote based on the reported results?

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