
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
Petya and Misha play the following game. Petya takes a coin in each hand: a 10-kopeck coin in one hand and a 15-kopeck coin in the other. After this, he multiplies the content of his left hand by 4, 10, 12, or 26, and the content of his right hand by 7, 13, 21, or 35. Then Petya adds the two resulting products and tells Misha the result. Knowing this result, can Misha determine in which hand Petya has the 10-kopeck coin (left or right)?

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