
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 triangle $\triangle ABC$, where $A$, $B$, and $C$ are the angles opposite to sides $a$, $b$, and $c$ respectively. Additionally, $c=\frac{5}{2}$, $b=\sqrt{6}$, and $4a-3\sqrt{6}\cos A=0$.

(1) Find the value of $a$;

(2) If $B=\lambda A$, find the value of $\lambda$.

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