
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 the ant starts at vertex  $A$  of regular hexagon  $ABCDEF$  and moves either right or left each move with equal probability. After  $35$  moves, what is the probability that she is on either vertex  $A$  or  $C$ ?

*2015 CCA Math Bonanza Lightning Round #5.3*

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