
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
Let a basketball player have a probability of $\frac{1}{2}$ for making a basket with each shot, and each shot be independent. Let $a_n$ denote the ratio of successful shots to total shots after $n$ shots. Find the probability of the event "$a_6 = \frac{1}{2}$ and $a_n \leq \frac{1}{2}$ for $n=1, 2, 3, 4, 5$".

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