
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 a die is rolled, it is equally likely for any one of the six faces to be on top. Construct the sequence $\{a_n\}$ such that 

$$
a_n = 
\begin{cases} 
1, & \text{when an odd number is on top on the } n\text{th roll} \\
-1, & \text{when an even number is on top on the } n\text{th roll}
\end{cases}
$$.

Define $S_n = a_1 + a_2 + \ldots + a_n$ (where $n \in \mathbb{N}^*$). Find the probability that $2 \leq S_6 \leq 4$.

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