
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 new set operation $\Delta: A\Delta B=\{x| x\in A$, and $x\notin B\}$. If $A=\{x|4x^{2}+9x+2 \lt 0\}$, $B=\{x| -1 \lt x \lt 2\}$, $M=B\Delta A$.  
$(1)$ Find the set $M$;  
$(2)$ Let the solution set of the inequality $(x-2a)(x+a-2) \lt 0$ be $P$. If $x\in P$ is a necessary condition for $x\in M$, find the range of real number $a$.

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