
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  $f\in C^1[a,b]$ ,  $f(a)=0$  and suppose that  $\lambda\in\mathbb R$ ,  $\lambda >0$ , is such that  $$ |f'(x)|\leq \lambda |f(x)| $$  for all  $x\in [a,b]$ . Is it true that  $f(x)=0$  for all  $x\in [a,b]$ ?

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