
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 the Lemon Kingdom, there are 2020 villages. Some pairs of villages are directly connected by paved roads. The road network is arranged so that for any two villages, there is exactly one way to travel from one to the other without traveling along any road twice. Agent Orange wants to fly over as many villages as possible in a helicopter. To maintain secrecy, he will not visit any village twice, and will not visit two consecutive villages that are directly connected by a road. How many villages can he be guaranteed to fly over? He can start from any village.

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