
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)\\) When \\(a=1\\), solve the inequality \\(f(x)+|2x-5| \geqslant 6\\).
\\((2)\\) If the function \\(g(x)=f(x)-|x-3|\\) has a range of \\(A\\), and \\([-1,2] \subseteq A\\), find the range of values for \\(a\\).

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