
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 $f\left( x \right)=x\left( {{e}^{x}}+1 \right)$,

(1) Find the equation of the tangent line to the graph of the function $y=f\left( x \right)$ at the point $\left(0,f\left(0\right)\right)$;

(2) If the function $g\left( x \right)=f\left( x \right)-a{{e}^{x}}-x$, find the maximum value of the function $g\left( x \right)$ on the interval $\left[1,2\right]$.

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