
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
When tossing a fair coin, the probability of getting heads or tails is $\frac{1}{2}$. If such a toss is repeated, the sequence $\{a_n\}$ is defined as follows: $a_n = \begin{cases} 1 & \text{if the }n\text{th toss results in heads} \\ -1 & \text{if the }n\text{th toss results in tails}\end{cases}$. Let $S_n = a_1 + a_2 + \ldots + a_n$, then the probability that $S_2 \neq 0$ and $S_6 = 0$ is \_\_\_\_\_\_.

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