
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
Define $a*b = 2 \times \left\{ \frac{a}{2} \right\} + 3 \times \left\{ \frac{a+b}{6} \right\}$, where the symbol $\{x\}$ represents the fractional part of $x$, such as $\{2.016\} = 0.016$. Then, calculate $1.4*3.2$ if the answer is represented as a decimal.

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