
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
A particle $Q$ on the number line starts from the origin and moves randomly either one unit to the left or one unit to the right each time, with the probability of moving left being $\frac{1}{3}$ and the probability of moving right being $\frac{2}{3}$. Let $X_{n}$ denote the real number corresponding to the position of point $Q$ after $n$ moves.<br/>$(1)$ Find the probability distribution and expectation of $X_{3}$ and $X_{4}$;<br/>$(2)$ When $n=10$, at which position is the probability highest for point $Q$ to be, and explain the reason.

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