
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
Calculate the mass of the plane curve \( y = \frac{x^{3}}{3} \) on the segment from \( x = 0 \) to \( x = 0.1 \) units of length, given that the linear density \( \rho \) depends on the coordinate \( x \) as follows: \( \rho(x) = 1 + x^{2} \).

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