
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 \(f(x)=|x+a|+|2x-1|\) where \(a \in \mathbb{R}\):
1. When \(a=1\), determine the solution set of the inequality \(f(x) \geqslant 2\).
2. If the solution set of \(f(x) \leqslant 2x\) includes \([ \frac {1}{2},1]\), find the range of possible values for \(a\).

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