
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 that the function f(x) is an even function defined on ℝ and is monotonically increasing on the interval [0, +∞), if the real number a satisfies f(log₂ a) + f(log₁₆ a) ≤ 2f(1), determine the range of a.

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