
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 school organized an "Environmental Knowledge" quiz competition, which was divided into five groups. It was stipulated that answering a question correctly would earn $50$ points, while answering a question incorrectly would deduct $10$ points. At the end of the event, the scorekeeper announced the scores of each group as follows:

|  Group 1  |  Group 2  |  Group 3  |  Group 4  |  Group 5  |
|:---------:|:---------:|:---------:|:---------:|:---------:|
|    $100$   |    $150$   |   $-400$  |    $350$   |   $-100$  |

$(1)$ By how many points did the first group exceed the second group?<br/>$(2)$ By how many points did the first group exceed the fifth group?

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