
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 $f(x) = |x - a|$, where $a \in \mathbb{R}$:
1. Find the range of values for $a$ when $1 \leq x \leq 3$ and $f(x) \leq 3$.
2. Find the minimum value of real number $a$ such that $f(x - a) + f(x + a) \geq 1 - a$ holds true for any $x \in \mathbb{R}$.

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