
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
Vasya arranges the natural numbers from 1 to 10 in the product \( a^{b} b^{c} c^{d} d^{e} e^{f} f^{g} g^{k} k^{l} l^{m} m^{a} \) (the same letters denote the same digits, different letters denote different digits). What is the highest power of two that this product can be divided by?

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