
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 platinum sphere weighs $p = 30$ grams in a vacuum. This sphere is immersed in mercury at $t = 100^{\circ}$C. The densities of both materials are known at $0^{\circ}$C, namely for platinum $d_{1} = 21.5$ and for mercury $d_{2} = 13.60$. The cubic thermal expansion coefficients are $a_{1} = 0.0000264$ for platinum and $a_{2} = 0.0001815$ for mercury. What is the weight of the platinum sphere in this mercury?

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