
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 the symbols $ \lt a$,$b \gt $ as the smaller of the two numbers $a$ and $b$, and the symbol "「$a$,$b$」" as the larger of the two numbers. For example, $ \lt 0$,$-1 \gt =-1$, and "「$9$,$7$」$=9$.<br/>$(1)$ Fill in the blanks: $ \lt -2$,$-\frac{3}{2} \gt =$______, "「$a^{2}-1$,$a^{2}$」$=$______；<br/>$(2)$ If $ \lt m$,$m-3 \gt +\frac{3}{2}\times $ "「$-\frac{1}{2}m$,$-\frac{1}{2}(m-1)$」$=-4$, find the value of $m$.

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