
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
Elza draws  $2013$  cities on the map and connects some of them with  $N$  roads. Then Elza and Susy erase cities in turns until just two cities left (first city is to be erased by Elza). If these cities are connected with a road then Elza wins, otherwise Susy wins. Find the smallest  $N$  for which Elza has a winning strategy.

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