
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
The function  $f$  is increasing and convex (i.e. every straight line between two points on the graph of  $f$  lies above the graph) and satisfies  $f(f(x))=3^x$  for all  $x\in\mathbb{R}$ . If  $f(0)=0.5$  determine  $f(0.75)$  with an error of at most  $0.025$ . The following are corrent to the number of digits given:

\[3^{0.25}=1.31607,\quad 3^{0.50}=1.73205,\quad 3^{0.75}=2.27951.\]

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