
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 $f(x) = |x - 10| - |x - 25|$, and the solution set for the inequality $f(x) < 10a + 10$ ($a \in \mathbb{R}$) is $\mathbb{R}$.

(1) Determine the range of values for the real number $a$.
(2) Find the minimum value of $2a + \frac{27}{a^2}$.

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