
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
How many solutions does the equation

$$
\{x\}^{2}=\left\{x^{2}\right\}
$$

have in the interval $[1, 100]$? ($\{u\}$ denotes the fractional part of $u$, which is the difference between $u$ and the largest integer not greater than $u$.)

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