
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) Two players are playing a game: on the table, there are 7 coins worth two pounds each and 7 coins worth one pound each. On each turn, a player is allowed to take coins worth no more than three pounds. The player who takes the last coin wins. Who will win with perfect play?

b) The same question if there are 12 coins worth two pounds each and 12 coins worth one pound each.

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