
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
Alloys of lead and tin are often used for soldering (i.e., for connecting and "welding" two pieces of metal). The most easily fusible of these alloys, known as "eutectic" or "tertnik," contains 36% Pb (about one-third) and 64% Sn. One day, a workshop needed eutectic alloy, but they did not have any. They also didn't have pure metals Pb and Sn. However, the workshop had two other alloys of these metals. The first alloy ("quarter-nik") contained 25% Pb, and the second alloy contained 60% Pb. How many grams of each of these alloys are needed to obtain 1 kg of eutectic alloy?

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