
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
If the force $F$ (in Newtons) that a spring experiences due to compression and the distance $L$ (in meters) it is compressed follow Hooke's Law, calculated as $F=KL$, and a force of 100 N compresses the spring by 10 cm, calculate the work done to compress the spring from its equilibrium position to 20 cm (within the elastic limit).

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