
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 the function $f(x) = |2x+1| - |x-2|$.  
(1) If the inequality $a \geq f(x)$ has real solutions for $x$, find the range of values for the real number $a$;  
(2) If for all $x \in \mathbb{R}$, $f(x) \geq -t^2 - \frac{5}{2}t - 1$ always holds, find the range of values for the real number $t$.

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