
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
There is a connected network with  $ 2008$  computers, in which any of the two cycles don't have any common vertex. A hacker and a administrator are playing a game in this network. On the  $ 1st$  move hacker selects one computer and hacks it, on the  $ 2nd$  move administrator selects another computer and protects it. Then on every  $ 2k\plus{}1th$  move hacker hacks one more computer(if he can) which wasn't protected by the administrator and is directly connected (with an edge) to a computer which was hacked by the hacker before and on every  $ 2k\plus{}2th$  move administrator protects  one more computer(if he can) which wasn't hacked by the hacker and is directly connected (with an edge) to a computer which was protected by the administrator before for every  $ k>0$ . If both of them can't make move, the game ends. Determine the maximum number of computers which the hacker can guarantee to hack at the end of the game.

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