
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 material and complete the questions:<br/>We call the largest integer not exceeding $x$ as the integer part of $x$, denoted as $\left[x\right]$, and we call $x-\left[x\right]$ as the decimal part of $x$, denoted as $\{x\}$, then $x=\left[x\right]+\{x\}$. For example: $\left[1.3\right]=1$, $\{1.3\}=0.3$, $1.3=\left[1.3\right]+\{1.3\}$;<br/>$(1)\{1.6\}=\_\_\_\_\_\_,\left[-1.6\right]=\_\_\_\_\_\_$;<br/>$(2)$ If $\left[x\right]=2\{x\}$, the value of $x$ is ______;<br/>$(3)3\left[x\right]+1=2\{x\}+x$, find the value of $x$.

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