
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
Positive numbers $a$ and $b$ satisfy the equation $2a + b = 1$. If $2\sqrt{ab} - 4a^2 - b^2 \leq t - \frac{1}{2}$ holds true, determine the range of values for the real number $t$.

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