
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 the function f(x) = |x + 1| - |ax - 3| (a > 0).
1. Find the solution set of the inequality f(x) > 1 when a = 2.
2. If the graph of y = f(x) forms a right triangle with the x-axis, find the value of a.

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