
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 $f(x) = |x-a| + |x+b|$ ($a>0$, $b>0$).

(Ⅰ) If $a=1$, $b=2$, solve the inequality $f(x) \leq 5$;

(Ⅱ) If the minimum value of $f(x)$ is 3, find the minimum value of $\frac{a^2}{b} + \frac{b^2}{a}$.

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