
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
For three numbers $a$, $b$, $c$, let $M\left\{ a,b,c \right\}$ represent the median of these three numbers, and let $\max \left\{ a,b,c \right\}$ represent the maximum of these three numbers. For example: $M\left\{ -5,0,3 \right\}=0$, $\max \left\{ -1,2,5 \right\}=5$, $\max \left\{ -2,-1,a\right\}=\left\{ \begin{array}{l} {a\left( a\geqslant-1\right)}\\{-1\left( a\lt-1\right)} \end{array}\right. $. Solve the problem: $M\left\{ \sin 30{}^\circ ,\cos 45{}^\circ ,\tan 60{}^\circ \right\}=$&nbsp;<u>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</u>&nbsp;. If $\max \left\{ 5,2x-3,-10-3x \right\}=5$, then the range of $x$ is&nbsp;<u>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</u>&nbsp;.<br/>

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