
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 $a=(4,3)$ and $b=(-1,2)$.

(1) Find the cosine of the angle $\theta$ between $a$ and $b$;

(2) If $(a-\lambda b)$ is perpendicular to $(2a+b)$, find the value of the real number $\lambda$.

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