
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  $f:\mathbb{R} \rightarrow \mathbb{R}$  such that: $\bullet$   $f(x)<2$  for all  $x\in (0,1)$ ; $\bullet$  for all real numbers  $x,y$  we have:  $$ max\{f(x+y),f(x-y)\}=f(x)+f(y) $$  Proposed by Navid Safaei

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