
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
Given the function $$f(x)=a^{x}+\log_{a}(x+1)$$  
(1) When $a=2$, find the maximum value of $f(x)$ for $x \in [0, 1]$;  
(2) When $0 < a < 1$, the sum of the maximum and minimum values of $f(x)$ on $x \in [0, 1]$ is $a$. Find the value of $a$.

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