
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 $f(x) = 45|x - a| + 45|x - 5|$.
1. Find the range of values for $a$ such that the inequality $f(x) \geq 3$ always holds.
2. When $a = 2$, find the solution set for the inequality $f(x) \geq x^2 - 8x + 15$.

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