
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
There are three cups of solution with equal weight, and their concentrations are $10 \%, 20 \%, 45 \%$ respectively. If $\frac{1}{2}$, $\frac{1}{4}$, and $\frac{1}{5}$ of the weights from the three cups are poured into a fourth empty cup in order, what is the concentration of the solution in the fourth cup? $\qquad$ $\%$.

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