
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 $f(x) = \ln(e^x + a)$ is an odd function with domain $\mathbb{R}$, and $g(x) = \lambda f(x)$.  
(1) Find the value of the real number $a$;  
(2) If $g(x) \leq x\log_2x$ holds for all $x \in [2, 3]$, find the range of values for $\lambda$.

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