
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
Given the universal set $U = \mathbb{R}$, set $M=\{x | (x+4)(x-6) \lt 0\}$, $N=\{x | x-5 \lt 0\}$.  
$(1)$ Find $M \cup N$ and $\overline{N}_\mathbb{R}$.  
$(2)$ Let $P=\{x | |x|=t\}$. If $P \subseteq M$, find the range of $t$.

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