
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
Andrew and Barry play the following game: there are two heaps with  $a$  and  $b$  pebbles, respectively. In the first round Barry chooses a positive integer  $k,$  and Andrew takes away  $k$  pebbles from one of the two heaps (if  $k$  is bigger than the number of pebbles in the heap, he takes away the complete heap). In the second round, the roles are reversed: Andrew chooses a positive integer and Barry takes away the pebbles from one of the two heaps. This goes on, in each round the two players are reversing the roles. The player that takes the last pebble loses the game.

Which player has a winning strategy?

*Submitted by András Imolay, Budapest*

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