
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
During the Double 11 shopping festival, Xiaozhang bought a box of crabs labeled as "$2$ taels each" weighing $5$ jin $(1$ jin $=10$ taels). When he got home, Xiaozhang's son found it fun and weighed each crab:<table><tbody><tr><td width="149">Deviation from standard weight $/$ taels</td><td width="60">$-0.3$</td><td width="60">$-0.2$</td><td width="60">$-0.1$</td><td width="60">$0$</td><td width="60">$0.1$</td><td width="60">$0.2$</td></tr><tr><td>Number of crabs</td><td>$1$</td><td>$2$</td><td>$3$</td><td>$1$</td><td>$4$</td><td>$2$</td></tr></tbody></table>$(1)$ How much larger is the largest crab in the box compared to the smallest one?<br/>$(2)$ By calculation, explain whether the total weight of this box of crabs exceeds or falls short of $5$ jin.

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