
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 $f(x) = e^x + a\cos x$ (where $e$ is the base of the natural logarithm).

(1) If the tangent line of $f(x)$ at $x=0$ passes through point $P(1,6)$, find the value of the real number $a$;

(2) When $x \in \left[0, \frac{\pi}{2}\right]$, $f(x) \geqslant ax$ always holds, find the range of values for the real number $a$.

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