
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 $f(x) = \sqrt{x^2 - 2x + 1} + |x + a|$.  
(1) When $a=2$, find the minimum value of $f(x)$.  
(2) When $x \in \left[\frac{2}{3}, 1\right]$, $f(x) \leq x$ always holds, find the range of values for $a$.

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