
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
In triangle $ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted by $a$, $b$, and $c$ respectively. If for any $\lambda \in R$, the inequality $|\lambda \overrightarrow{BC} - \overrightarrow{BA}| \geq | \overrightarrow{BC}|$ always holds, then the maximum value of $\frac{c}{b} + \frac{b}{c}$ is __________ .

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