
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
After defeating Kashchei, Ivan demanded gold to redeem Vasilisa from the robbers. Kashchei took him to a cave and said: "In the chest, there are gold bars. But you can't just take them: they are enchanted. You must transfer one or more bars to your bag. Then I will transfer one or more bars from your bag back to the chest, but necessarily a different number. We will take turns transferring: you to the bag, I to the chest, each time a different number. When further transferring becomes impossible, you can take your bag with the bars." What is the maximum number of bars Ivan can take, regardless of Kashchei's actions, if there are initially a) 13; b) 14 gold bars in the chest? How can he achieve this?

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