
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 plane electrostatic field between two grounded parallel planes (\(0 < \boldsymbol{y} < h\)) is generated by linear sources, whose intrinsic field in an unbounded space is \(\vec{E}\).

Find the density distribution of induced charges on the surface of each plate \(\sigma_{0}(x)\) and \(\sigma_{h}(x)\).

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