
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 that the line $l: y=kx+b$ is the common tangent line of the functions $f\left(x\right)=ax^{2}(a \gt 0)$ and $g\left(x\right)=e^{x}$. If $\left(1,f\left(1\right)\right)$ is the point of tangency between the line $l$ and the function $f\left(x\right)$, then $b=$____.

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