
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
After learning rational numbers, Xiao Yuan developed a strong interest in operations. With the help of the operation definitions of rational numbers, he defined a new operation "$\triangle$", with the rule: $a\triangle b=ab+2a$. Please help Xiao Yuan calculate the value of $-3\triangle (-4\triangle \frac{1}{2})$.

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