
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
The International Conference of Multi-legged Creatures is held at the top of the Glass Mountain. The participants have \( a_{1}, \ldots, a_{n} \) legs, all of which are positive even numbers. The Glass Mountain is slippery, and the creatures gathering at the base of the mountain can only ascend if they wear special climbing shoes on at least half of their legs. Knowing that climbing shoes must be worn on the legs to ascend and descend the mountain, what is the minimum number of shoes required for all the conference participants to ascend the mountain?

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