
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 certain type of food produced by a food factory is labeled as "net weight $150\pm 4$ grams". To check whether the quality of the food in the bag meets the standard, $20$ bags of food are randomly selected. Each bag is labeled with a standard weight of $150$ grams, with the excess and deficiency of $150$ grams represented by positive and negative numbers, respectively. The records are as follows:

| Difference from Standard Weight (grams) | $-6$ | $-2$ | $0$ | $+1$ | $+2$ | $+4$ | $+5$ |
|-----------------------------------------|------|------|----|------|------|------|------|
| Number of Bags                           | $1$  | $3$  | $8$| $4$  | $1$  | $2$  | $1$  |

$(1)$ How many bags among the $20$ bags of food are qualified?<br/>$(2)$ What is the average weight of these $20$ bags of food in grams?

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