
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
In digital communication, signals are sequences composed of the digits "$0$" and "$1$". Signals are transmitted continuously $n$ times, with each transmission of "$0$" and "$1$" being equally likely. Let the number of times "$1$" is transmitted be denoted by $X$.<br/>$(1)$ When $n=6$, find $P\left(X\leqslant 2\right)$;<br/>$(2)$ Given the Chebyshev's inequality: For any random variable $Y$, if its mean $E\left(Y\right)$ and variance $D\left(Y\right)$ both exist, then for any positive real number $a$, we have $P(|{Y-E(Y)}|＜a)≥1-\frac{{D(Y)}}{{{a^2}}}$. According to this inequality, a lower bound estimate can be made for the probability of the event "$|Y-E\left(Y\right)| \lt a$". In order to have at least $98\%$ confidence that the frequency of transmitting the signal "$1$" is between $0.4$ and $0.6$, estimate the minimum value of the number of signal transmissions $n$.

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