
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 $f(x)=\sin({ωx}+φ)+1(\omega > 0,-\frac{π}{2} < φ < \frac{π}{2})$ with a minimum positive period of $π$, and its graph passing through point $P(0,1)$:

1. Find the analytical expression of the function $f(x)$;
2. Let $g(x)=f(x)+\cos 2x-1$. After shifting all points on the graph of function $g(x)$ to the right by $\frac{π}{4}$ units, the resulting graph is a monotonous function in the interval $(0,m)$. Find the maximum value of the real number $m$.

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