
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
From a batch of bagged food, $20$ bags were sampled. If each bag of food has a standard weight of $500$ grams, the differences from the standard weight are recorded using positive and negative numbers as follows:

| Difference from Standard Weight (grams) | $-20$ | $-5$ | $0$ | $2$ | $3$ | $10$ |
|----------------------------------------|-------|------|----|----|----|-----|
| Number of Bags                         | $4$   | $1$  | $3$| $4$| $5$| $3$ |

$(1)$ How many grams more is the bag with the maximum weight compared to the bag with the minimum weight among the $20$ bags?

$(2)$ What is the total weight of the $20$ bags of food?

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