
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 that the function $f(x) = x \ln(x + \sqrt{2a + x^2}) \ (a > 0)$ is an even function.

1. Find the value of $a$.
2. Find the range of the function $g(x) = ax^2 + 2x + 1$ on the interval $[-6, 3]$.

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