
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 a flood control emergency, a large oil tank drifting downstream from upstream needs to be exploded by shooting. It is known that there are only $5$ bullets. The first hit can only cause the oil to flow out, and the second hit can cause an explosion. Each shot is independent, and the probability of hitting each time is $\frac{2}{3}$.

$(1)$ Calculate the probability that the oil tank will explode;

$(2)$ If the oil tank explodes or the bullets run out, the shooting will stop. Let $X$ be the number of shots. Calculate the probability that $X$ is not less than $4$.

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