
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
Let proposition p denote that the function y=(a-1)^x is increasing with respect to x; and proposition q denote the inequality -3^x ≤ a is true for all positive real numbers x. If the proposition "p ∨ q" (p or q) is true, and "p ∧ q" (p and q) is false, determine the range of the real number a.

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