
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

100 identical metal spheres with a radius of \( R = 1 \) mm are connected by equal conductive segments into a chain, where each segment of the connecting wire has a length of \( l = 50 \) cm, which is much greater than the radius of the sphere. Then, the resulting structure was placed in a uniform electric field with a known intensity \( E = 1000 \text{ V/m} \). The spheres are arranged in a line parallel to the intensity vector. What are the magnitudes of the charges induced on the end spheres in the chain?

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