
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 that $\{x\}$ and $[x]$ represent the fractional and integer parts of the number $x$, respectively. The integer part of the number $x$ is the largest integer not greater than $x$, and $\{x\} = x - [x]$. Find $x$ such that $4x^2 - 5[x] + 8\{x\} = 19$.

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