
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 the production process of a ceramic factory, the weights (unit: $kg$) of 100 imitation handicrafts were measured as shown in the table below:

| Group | $\left[2.20,2.30\right)$ | $\left[2.30,2.40\right)$ | $\left[2.40,2.50\right)$ | $\left[2.50,2.60\right)$ | $\left[2.60,2.70\right)$ | $\left[2.70,2.80\right)$ | Total |
|-------|--------------------------|--------------------------|--------------------------|--------------------------|--------------------------|--------------------------|-------|
| Frequency | 4 | 26 | $a$ | 28 | 10 | 2 | 100 |
| Frequency | 0.04 | | | $b$ | | | |

$(1)$ Find the values of the real numbers $a$ and $b$ in the frequency distribution table.  
$(2)$ If 2 handicrafts are randomly selected from the ones with weights in the range $\left[2.60,2.80\right)$, find the probability that both selected handicrafts have weights in the range $\left[2.70,2.80\right)$.

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