
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
Solve in the set  $R$  the equation  $$ 2 \cdot [x] \cdot  \{x\} = x^2 - \frac32 \cdot x - \frac{11}{16} $$  where  $[x]$  and  $\{x\}$  represent the integer part and the fractional part of the real number  $x$ , respectively.

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