
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
A boy named Seryozha saw two dragons with two heads each, whose heads had become entangled. The dragons can either be truthful, in which case both heads always tell the truth, or deceitful, in which case both heads always lie. Seryozha decided to help the dragons untangle their heads. To do this, he needs to know which heads belong to which dragon. He asked the dragons, and the heads said the following:

First head: "I am a truthful head";
Second head: "The third head is my original head";
Third head: "The second head is not my original head";
Fourth head: "The third head is a liar."

Which heads belong to which dragons?

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