
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
Read the following and then answer the questions: For three numbers $a$, $b$, $c$, we use symbols to represent the largest and smallest numbers among them. We define $\min \{a,b,c\}$ as the smallest number among the three, and $\max \{a,b,c\}$ as the largest number among the three. For example: $\min \{-1,2,3\}=-1$, $\max \{-1,2,3\}=3$;<br/>$(1)$ $\max \{x,1+x,x-1\}=$____;<br/>$(2)$ If $\min \{5,5-2x,2x+5\}=\max \{2,x+1,2x\}$, then the value of $x$ is ____.

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