
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 propositions p: "For all $x$ in $[0, 1]$, $a \geq 2^x$", and q: "There exists an $x$ in $\mathbb{R}$ such that $x^2 + 4x + a = 0", determine the range of the real number $a$ if the conjunction of propositions p and q is true.

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