
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 $f(x)=|x|+|x+1|$.
(1) If $\forall x \in \mathbb{R}$, it always holds that $f(x) \geqslant \lambda$, find the range of values for the real number $\lambda$;
(2) If $\exists m \in \mathbb{R}$, such that $m^{2}+2m+f(t)=0$ holds, find the range of values for the real number $t$.

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