
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
**a)** Solve in  $ \mathbb{R} $  the equation  $ 2^x=x+1. $ **b)** If a function  $ f:\mathbb{R}\longrightarrow\mathbb{R} $  has the property that   $$  (f\circ f)(x)=2^x-1,\quad\forall x\in\mathbb{R} ,  $$  then  $ f(0)+f(1)=1. $ 

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