
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
When x < 0, f(x) = -x^2 + x, and f(x) is an odd function. Determine the range of values for the real number a such that the inequality f(x) - x ≤ 2log_a x, where a > 0 and a ≠ 1, holds for all x in (0, 1/√2].

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