
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
Find all functions \( f: \mathbf{R}_{+} \rightarrow \mathbf{R}_{+} \) that satisfy \( f(x) < 2x - \frac{x}{1 + x^{\frac{3}{2}}} \) for \( x > 0 \) and \( f(f(x)) = \frac{5}{2} f(x) - x \).

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