
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 for all $x \in \mathbb{R}$, it always holds that $f(x) \geq \lambda$, find the range of the real number $\lambda$;
(2) If there exists $m \in \mathbb{R}$, such that $m^2 + 2m + f(t) = 0$ holds, try to find the range of the real number $t$.

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