
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
Alice initially paid $A$ dollars, while Bob paid $B$ dollars, where $A > B$. At the end of their trip, they incurred an additional mutual expense of $C$ dollars, which Bob paid entirely. They agreed that Alice should reimburse Bob for half of this last expense. Calculate the amount of money that Alice must give to Bob to equally share the total costs.

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