
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
Let  $a,b\in\mathbb{R},~a>1,~b>0.$  Find the least possible value for  $\alpha$  such that :  $$ (a+b)^x\geq a^x+b,~(\forall)x\geq\alpha. $$  

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