
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 $g(x) = (a + 1)^{x - 2} + 1 \ (a > 0)$, its graph always passes through point $A$, which also lies on the graph of the function $f(x) = \log_{\sqrt{3}}(x + a)$.

1. Find the value of the real number $a$.
2. Solve the inequality $g(x) > 3$.

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