
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
For any two numbers \( x \) and \( y \), a new operation * is defined as:
\[ x * y = \frac{x \times y}{m \times x + 2 \times y} \]
(where \( m \) is a determined number). If \( 1 * 2 = \frac{2}{5} \), then find \( m \), and calculate \( 2 * 6 \).

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