
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 the function $f(x)=x^{3}+ax^{2}+2x-a^{2}$, if for any $x_{1}$, $x_{2}\in \left[1,2\right]$, where $x_{1} \lt x_{2}$, the inequality $\frac{{f({{x_1}})-f({{x_2}})}}{{{x_1}-{x_2}}}＜2$ holds, then the maximum value of the real number $a$ is ____.

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